A127964 - OEIS

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

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OFFSET

1,3

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]

LINKS

Table of n, a(n) for n=1..41.

FORMULA

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

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

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 *)

CROSSREFS

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

Sequence in context: A018519 A050054 A018371 * A269929 A364238 A085370

Adjacent sequences: A127961 A127962 A127963 * A127965 A127966 A127967

KEYWORD

nonn,base,more,changed

AUTHOR

Artur Jasinski, Feb 09 2007

EXTENSIONS

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

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

STATUS

approved