Intended for: February 13, 2012
Timetable
- First draft entered by Alonso del Arte on November 13, 2011 ✓
- Draft reviewed by Daniel Forgues on February 02, 2017 ✓
- Draft to be approved by January 13, 2012
Yesterday's SOTD * Tomorrow's SOTD
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A066340:
Fermat’s triangle:
, for
and
.
(Concatenated rows of Fermat’s triangle.)
-
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{1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, ... }
Fermat’s triangle
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2
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1
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1
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3
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1
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1
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2
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4
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1
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0
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1
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2
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5
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1
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1
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1
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1
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4
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6
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1
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4
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3
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4
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1
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13
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7
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1
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1
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1
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1
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1
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1
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6
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8
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1
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0
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1
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0
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1
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0
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1
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4
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9
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1
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1
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0
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1
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1
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0
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1
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1
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6
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10
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1
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6
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1
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6
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5
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6
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1
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6
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1
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33
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11
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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10
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12
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1
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4
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9
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4
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1
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0
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1
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4
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9
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4
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1
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38
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13
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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12
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14
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1
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8
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1
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8
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1
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8
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7
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8
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1
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8
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1
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8
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1
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61
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15
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1
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1
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6
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1
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10
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6
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1
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1
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6
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10
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1
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6
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1
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1
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52
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16
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1
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0
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1
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0
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1
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0
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1
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0
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1
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0
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1
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0
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1
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0
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1
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8
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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Per
Fermat’s little theorem, the rows corresponding to
prime consist of all
1s, although the converse is not true: rows corresponding to
composite which consist of all
1s are the
Carmichael numbers. Also, the
prime powers consist only of ones and zeros, e.g.
- powers of 2: 1, 0 (repeated pattern);
- powers of 3: 1, 1, 0 (repeated pattern);
- ...
Is the converse also false? That is, are there “pseudoprimepowers” to all bases, i.e. giving a repeated pattern identical to some prime power?
A?????? Row sums of Fermat’s triangle:
, for
.
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{1, 2, 2, 4, 13, 6, 4, 6, 33, 10, 38, 12, 61, 52, 8, ...}