A307509 Using the mapping in A306979, the sum of powers of 2 where the exponents are the digits of the previous term, a(n) is the number of steps to reach the end of the first cycle.

35, 34, 33, 36, 32, 15, 15, 30, 35, 25, 37, 33, 15, 38, 25, 17, 31, 35, 24, 35, 15, 16, 36, 16, 15, 29, 41, 27, 16, 6, 26, 38, 15, 32, 16, 37, 28, 20, 23, 22, 36, 25, 16, 16, 16, 22, 16, 18, 21, 24, 33, 17, 29, 37, 22, 16, 17, 10, 6, 17, 18, 31, 41, 28, 15, 17, 30, 8, 40, 15

Offset

0,1

Comments

There are only four eventual cycles as cited in A306979:

- (148, 274) (length = 2);

- (98, 768, 448, 288, 516) (length = 5);

- (70, 129, 518, 290, 517, 162) (length = 6);

- (5, 32, 12, 6, 64, 80, 257, 164, 82, 260, 69, 576, 224, 24, 20) (length = 15).

First occurrence of length k or -1 if no such length occurs for k=2,3,4,...: 148, 184, 1578, 98, 29, 126, 67, 106, 57, 299, 2399, -1, -1, 5, 21, 15, 47, 136, 37, 48, 39, 38, 18, 9, 30, 27, 36, 25, 7, 16, 4, 2, 1, 0, 3, 10, 13, 203, 68, 26, 134, 127, 2357, ..., .

Links

Table of n, a(n) for n=0..69.

Example

a(0) = 35 since the mapping as described in A306979 is that sequence's first 35 terms;
a(1) = 34 since it is the sequence above less the first term;
a(2) = 33 since it is the sequence above less the first two terms;
a(29) = 6 since the sequence is {29 -> 516 -> 98 -> 768 -> 448 -> 288 -> 516 -> ...};
a(184) = 3 since the sequence is {184 -> 274 -> 148 -> 274}; etc.

Mathematica

g[n_] := Plus @@ (2^IntegerDigits@ n); f[n_] := Length[ NestWhileList[ g@# &, n, UnsameQ, All]] - 1; Array[f, 70, 0]

Crossrefs

Cf. A306979.

Sequence in context: A267394 A022991 A023477 * A291654 A257948 A142728

Adjacent sequences: A307506 A307507 A307508 * A307510 A307511 A307512

Keyword

nonn,base

Author

Jianing Song and Robert G. Wilson v, Apr 11 2019

Status

approved