A109733 - OEIS

%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