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

Author

Rémy Sigrist, Jan 17 2020

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A000961, A162439, A331362.

Programs

PARI

See Links section.

Formula

a(n) >= A162439(n).

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