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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 21 12:49 EDT 2024. Contains 372736 sequences. (Running on oeis4.)