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A109733
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Sequence is its own base-10 ASCII representation.
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3
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53, 51, 53, 49, 53, 51, 52, 57, 53, 51, 53, 49, 53, 50, 53, 55, 53, 51, 53, 49, 53, 51, 52, 57, 53, 51, 53, 48, 53, 51, 53, 53, 53, 51, 53, 49, 53, 51, 52, 57, 53, 51, 53, 49, 53, 50, 53, 55, 53, 51, 53, 49, 53, 51, 52, 56, 53, 51, 53, 49, 53, 51, 53, 51, 53, 51, 53, 49, 53
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OFFSET
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1,1
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COMMENTS
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Out of the digits 0,1,...,9, 5 is the only one whose ASCII representation, converted to base 10, begins with itself. So this sequence is the unique one with this property. - N. J. A. Sloane, Aug 25 2015
The octal version of this idea is simply 66,66,66,66,.., not interesting.
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LINKS
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FORMULA
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I conjecture that a(n) = 53 when n is congruent to 1, 3 or 5 (mod 8) and a(n) = 51 when n is congruent to 2 (mod 8). - Jonathan Cross (jcross(AT)juggler.net), Oct 14 2005
a(n) = (if valuation(n/2^v + 1, 2) mod 5 = 3 then 56 else 57) - 2*((v-3) mod 5), where v = valuation(n,2), i.e., n = (2s+1)*2^v. (Translation of my PARI code from June 2011.) - M. F. Hasler, Feb 02 2016
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EXAMPLE
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We use the following table, giving digit d, ASCII equivalent in base 8, ASCII equivalent in base 10:
.0..1..2..3..4..5..6..7..8..9
60 61 62 63 64 65 66 67 70 71
48 49 50 51 52 53 54 55 56 57
We must start with 5 (see comment above), so the sequence grows like this:
5
53
53 51
53 51 53 49
53 51 53 49 53 51 52 57
...
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PROG
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(PARI) a(n) = (valuation(1+n>>n=valuation(n, 2), 2)%5!=3)+56-(n-3)%5*2 \\ M. F. Hasler, Jun 20 2011
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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More terms from Jonathan Cross (jcross(AT)juggler.net), Oct 14 2005
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STATUS
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approved
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