A127964 Number of 0's in the binary expansion of A127962(n).

0, 1, 2, 4, 5, 7, 8, 10, 14, 20, 29, 38, 49, 62, 82, 94, 98, 155, 172, 349, 853, 1307, 1768, 2902, 5249, 5344, 5638, 6194, 7238, 21367, 41668, 47683, 58618, 63514, 69467, 70538, 133507, 134992, 187159, 493094, 2015698

Offset: 1

Author

Artur Jasinski, Feb 09 2007

Keywords

• nonn
• base
• more

Comments

Apparently numbers k such that (2^(2*k+3)+1)/3 is prime. - James R. Buddenhagen, Apr 14 2011 [This is true. See the second formula. - Amiram Eldar, Oct 13 2024]

Crossrefs

Cf. A000978, A000979, A023416, A127962, A127961, A000979, A000978, A124400, A126614, A127955, A127956, A127957, A127958, A127936.

Programs

Mathematica

b = {}; Do[c = 1 + Sum[2^(2n - 1), {n, 1, x}]; If[PrimeQ[c], AppendTo[b, c]], {x, 0, 1000}]; a = {}; Do[AppendTo[a, FromDigits[IntegerDigits[b[[x]], 2]]], {x, 1, Length[b]}]; d = {}; Do[AppendTo[d, DigitCount[a[[x]], 10, 0]], {x, 1, Length[a]}]; d
(Select[Prime[Range[200]], PrimeQ[(2^# + 1)/3] &] - 3)/2 (* Amiram Eldar, Oct 13 2024 *)

Formula

a(n) = A023416(A000979(n)). - Michel Marcus, Nov 07 2013

a(n) = (A000978(n)-3)/2. - Amiram Eldar, Oct 13 2024

Extensions

a(22)-a(29) from Vincenzo Librandi, Mar 31 2012

a(30)-a(41) from Amiram Eldar, Oct 13 2024