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A102371
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Numbers missing from A102370.
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14
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1, 2, 7, 12, 29, 62, 123, 248, 505, 1018, 2047, 4084, 8181, 16374, 32755, 65520, 131057, 262130, 524279, 1048572, 2097133, 4194286, 8388587, 16777192, 33554409, 67108842, 134217711, 268435428, 536870885
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Indices of negative numbers in A103122.
Write numbers in binary under each other; start at 2^k, read in upward direction with the first bit omitted and convert to decimal:
. . . . . . . . . . 0
. . . . . . . . . . 1
.. . . . . . . . . 10 < -- Starting here, the upward diagonal (first bit omitted) reads 1 -> 1
.. . . . . . . . . 11
. . . . . . . . . 100 < -- Starting here, the upward diagonal (first bit omitted) reads 10 -> 2
. . . . . . . . . 101
. . . . . . . . . 110
. . . . . . . . . 111
.. . . . . . . . 1000 < -- Starting here, the upward diagonal (first bit omitted) reads 111 -> 7
. . . . . . . . .1001
Thus a(n) = A102370(2^n - n) - 2^n.
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REFERENCES
| David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
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LINKS
| David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
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FORMULA
| a(n) = -n + Sum_{ k >= 1, k == n mod 2^k } 2^k. - N. J. A. Sloane (njas(AT)research.att.com) and David Applegate (david(AT)research.att.com), Mar 22 2005. E.g. a(5) = -5 + 2^1 + 2^5 = 29.
a(2^k + k) -a(k) = 2^(2^k + k) - 2^k, with k>= 1.
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MAPLE
| A102371:= proc (n) local t1, l; t1 := -n; for l to n do if `mod`(n-l, 2^l) = 0 then t1 := t1+2^l end if end do; t1 end proc;
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CROSSREFS
| Cf. A102370, A103530, A103581, A103582, A103583.
Sequence in context: A059329 A177747 A175879 * A007230 A059053 A032025
Adjacent sequences: A102368 A102369 A102370 * A102372 A102373 A102374
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KEYWORD
| nonn,base,changed
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 13 2005
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EXTENSIONS
| More terms from Benoit Cloitre, Mar 20 2005
a(16) to a(22) from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 21 2005
a(15) to a(29) from David Applegate (david(AT)research.att.com), Mar 22 2005
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