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%I #29 Dec 31 2020 02:20:20
%S 53,51,53,49,53,51,52,57,53,51,53,49,53,50,53,55,53,51,53,49,53,51,52,
%T 57,53,51,53,48,53,51,53,53,53,51,53,49,53,51,52,57,53,51,53,49,53,50,
%U 53,55,53,51,53,49,53,51,52,56,53,51,53,49,53,51,53,51,53,51,53,49,53
%N Sequence is its own base-10 ASCII representation.
%C 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
%C The octal version of this idea is simply 66,66,66,66,.., not interesting.
%H David W. Wilson, <a href="/A109733/b109733.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F 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
%F 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
%e We use the following table, giving digit d, ASCII equivalent in base 8, ASCII equivalent in base 10:
%e .0..1..2..3..4..5..6..7..8..9
%e 60 61 62 63 64 65 66 67 70 71
%e 48 49 50 51 52 53 54 55 56 57
%e We must start with 5 (see comment above), so the sequence grows like this:
%e 5
%e 53
%e 53 51
%e 53 51 53 49
%e 53 51 53 49 53 51 52 57
%e ...
%o (PARI) a(n) = (valuation(1+n>>n=valuation(n,2),2)%5!=3)+56-(n-3)%5*2 \\ _M. F. Hasler_, Jun 20 2011
%Y See A109648 for another version.
%K easy,nonn,base
%O 1,1
%A _N. J. A. Sloane_ and _Nadia Heninger_, Aug 10 2005
%E More terms from Jonathan Cross (jcross(AT)juggler.net), Oct 14 2005
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