A331469 a(n) is the greatest value of the form p_1 + ... + p_k where p_1, ..., p_k are powers of primes and such that the concatenation of the binary representations of p_1, ..., p_k equals the binary representation of n.

1, 2, 3, 4, 5, 3, 7, 8, 9, 4, 11, 5, 13, 5, 8, 16, 17, 6, 19, 6, 7, 7, 23, 9, 25, 5, 27, 7, 29, 9, 31, 32, 17, 10, 18, 8, 37, 11, 20, 10, 41, 6, 43, 9, 15, 13, 47, 17, 49, 7, 26, 7, 53, 15, 28, 11, 26, 7, 59, 11, 61, 10, 32, 64, 33, 18, 67, 12, 13, 19, 71, 12

Offset

1,2

Comments

We can always split the binary representation of a number into powers of 2, so the sequence is well defined.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, PARI program for A331469

Index entries for sequences related to binary expansion of n

Formula

a(n) >= A162439(n).

a(n) <= n with equality iff n is a power of a prime.

Example

For n = 22:
- the binary representation of 22 is "10110",
- we can split it into "10" and "1" and "10" (2^1 and 2^0 and 2^1),
- or into "101" and "10" (5^2 and 2^1),
- hence a(22) = max(5, 7) = 7.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000961, A162439, A331362.

Sequence in context: A335791 A071829 A229998 * A067620 A343253 A330741

Adjacent sequences: A331466 A331467 A331468 * A331470 A331471 A331472

Keyword

nonn,base

Author

Rémy Sigrist, Jan 17 2020

Status

approved