A023396 If any odd power of 2 ends with k 1's and 2's, they must be the first k terms of this sequence in reverse order.

2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

2^1 ends in 2;
2^5 ends in 32;
2^9 ends in 512;
2^13 ends in 8192;
2^89 ends in ...562112.
There exists a power of two ending in 12, so for n = 3 the choice for a(3) = 1 or a(3) = 2 comes from the existence of a power of two ending in either 112 or 212. As 112 is divisible by 2^n = 8 (and 212 is not) a(3) = 1. - David A. Corneth, Jun 11 2020

Prog

(PARI) first(n) = my(f = 2, pow10 = 1, pow2 = 2); { for(i = 2, n, pow10*=10; pow2<<=1; c1 = pow10 + f; if(c1 % pow2 == 0, f = c1, c2 = 2*pow10 + f; if(c2 % pow2 == 0, f = c2 ) ) ); Vecrev(digits(f)) } \\ David A. Corneth, Jun 11 2020

Crossrefs

Cf. A053312, A126933.

Sequence in context: A293433 A177025 A265210 * A091221 A106495 A100428

Adjacent sequences: A023393 A023394 A023395 * A023397 A023398 A023399

Keyword

nonn,easy,base

Author

David W. Wilson

Extensions

Definition corrected by Gerry Leversha, Mar 17 2007

Status

approved