A109733 Sequence is its own base-10 ASCII representation.

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

Offset: 1

Author

N. J. A. Sloane and Nadia Heninger, Aug 10 2005

Keywords

• easy
• nonn
• base

Comments

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.

Examples

			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
  ...
		

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are fixed points of mappings

Crossrefs

See A109648 for another version.

Programs

PARI

a(n) = (valuation(1+n>>n=valuation(n,2),2)%5!=3)+56-(n-3)%5*2  \\ M. F. Hasler, Jun 20 2011

Formula

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

Extensions

More terms from Jonathan Cross (jcross(AT)juggler.net), Oct 14 2005