A034937 -id:A034937 - cp's OEIS frontend

A034938 Primes p such that (p-3)/2 is a prime of the form 6k-1.

13, 37, 61, 97, 109, 181, 229, 277, 337, 349, 397, 457, 541, 709, 769, 937, 1009, 1021, 1117, 1129, 1201, 1237, 1297, 1321, 1489, 1549, 1597, 1621, 1657, 1777, 1861, 2029, 2221, 2377, 2389, 2437, 2521, 2557, 2617, 2749, 2857, 3001, 3049

Offset: 1

Jud McCranie

Related to hyperperfect numbers of a certain form (form 1, theorem 1 in "A Study of Hyperperfect Numbers").

Robert Price, Table of n, a(n) for n = 1..10000
J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

Cf. A038536 and A034937.

Select[Prime[Range[500]],Mod[(#-3)/2,6]==5&&PrimeQ[(#-3)/2]&] (* Harvey P. Dale, Jul 27 2019 *)

Definition corrected by Jud McCranie, Jul 26 2019

A382242 Decimal expansion of Gamma(1/4)^2/(8sqrt(2Pi)).

Original entry on oeis.org

6, 5, 5, 5, 1, 4, 3, 8, 8, 5, 7, 3, 0, 2, 9, 9, 5, 2, 6, 1, 6, 2, 0, 9, 8, 9, 7, 4, 7, 2, 7, 7, 9, 8, 5, 3, 4, 2, 0, 6, 8, 8, 7, 3, 7, 8, 5, 7, 9, 0, 5, 7, 9, 0, 7, 0, 4, 2, 0, 5, 4, 2, 5, 9, 5, 0, 1, 9, 7, 6, 4, 6, 7, 6, 7, 6, 0, 3, 5, 6, 2, 5, 5, 7, 5, 7, 3, 8, 8, 3, 2, 4, 0, 3, 5, 7, 2, 7, 3, 3, 6, 1, 5, 3, 3, 9, 3, 8, 1, 6, 7, 9, 4, 5, 8

Offset: 0

R. J. Mathar, Mar 19 2025

			0.6555143885730299526162098974727798534...

Leyda Almodovar, Victor H. Moll, Hadrian Quan, Fernando Roman, Eric Rowland, and Michole Washington, Infinite products arising in paperfolding, JIS 19 (2016), Article 16.5.1, eq. (72).

Cf. A034937, A068466, A231863, A005843, A005408.

Digits := 120 ; GAMMA(1/4)^2/8/sqrt(2*Pi) ; evalf(%) ;

RealDigits[Gamma[1/4]^2/(8*Sqrt[2*Pi]), 10, 120][[1]] (* Amiram Eldar, Mar 20 2025 *)

Equals A068466^2 *A231863 /8.

Equals Product_{n>=1} (A005843(n)/A005408(n))^A034947(n).

cp's OEIS Frontend

A034938 Primes p such that (p-3)/2 is a prime of the form 6k-1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A382242 Decimal expansion of Gamma(1/4)^2/(8sqrt(2Pi)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

cp's OEIS Frontend

A034938 Primes p such that (p-3)/2 is a prime of the form 6k-1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A382242 Decimal expansion of Gamma(1/4)^2/(8*sqrt(2*Pi)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A382242 Decimal expansion of Gamma(1/4)^2/(8sqrt(2Pi)).