A278032 a(n) is the smallest positive integer not already in the sequence such that Sum_{i=1..n} binary_weight(a(i)) is prime.

3, 1, 5, 6, 15, 9, 23, 10, 27, 63, 12, 95, 29, 17, 30, 111, 119, 18, 123, 39, 20, 125, 43, 126, 255, 45, 24, 46, 33, 51, 16383, 53, 159, 34, 1023, 36, 175, 183, 54, 187, 189, 40, 1535, 48, 57, 65, 4095, 6143, 58, 66, 60, 190, 68, 1791, 207, 215, 219, 72, 221, 71

Offset

1,1

Comments

A binary analog of A269415.

Clearly 1 is the only term of odd weight that can appear, and if it is true (which is not presently known) that there infinitely many prime gaps of 2, 4, 6, 8, etc. then every number of even weight will appear.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

a[1] = 3; a[n_] := a[n] = Module[{k = 1, s = Sum[DigitCount[a[i], 2, 1], {i, 1, n - 1}]}, While[!FreeQ[Array[a, n - 1], k] || !PrimeQ[s + DigitCount[k, 2, 1]], k++]; k]; Array[a, 100] (* Amiram Eldar, Jul 18 2023 *)

Crossrefs

Cf. A000120 (binary weight), A269415.

Sequence in context: A256504 A205713 A254344 * A016600 A130418 A038871

Adjacent sequences: A278029 A278030 A278031 * A278033 A278034 A278035

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 11 2016

Extensions

a(13) corrected by Chai Wah Wu, Nov 11 2016

More terms from Chai Wah Wu, Nov 11 2016

Status

approved