A038536 -id:A038536 - cp's OEIS frontend

A034936 Numbers k such that 3*k + 4 is prime.

1, 3, 5, 9, 11, 13, 19, 21, 23, 25, 31, 33, 35, 41, 45, 49, 51, 53, 59, 63, 65, 69, 73, 75, 79, 89, 91, 93, 101, 103, 109, 111, 115, 121, 123, 125, 131, 135, 139, 143, 145, 151, 153, 161, 165, 173, 179, 181, 189, 191, 199, 201, 203, 205, 209, 213, 219, 223, 229

Offset: 1

Jud McCranie

Related to hyperperfect numbers of a certain form.

Daniel Starodubtsev, 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 A002476.
A002476 gives primes, A091178 gives prime index.
a(n) = A024892(n) - 1 = 2*A024899(n) - 1.
a(n) = A153183(n) - 2 = A107303(n) - 3.

[n: n in [1..1000] |IsPrime(3*n+4)] // Vincenzo Librandi, Nov 17 2010

lst={};Do[p=n+(n+1)+(n+3);If[PrimeQ[p],AppendTo[lst,n]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, May 22 2009 *)
Select[Range[300],PrimeQ[3#+4]&] (* Harvey P. Dale, Aug 25 2016 *)

is(n)=isprime(3*n+4) \\ Charles R Greathouse IV, Jul 02 2013

A034934 Numbers k such that (3*k + 1)/2 is prime.

Original entry on oeis.org

1, 3, 7, 11, 15, 19, 27, 31, 35, 39, 47, 55, 59, 67, 71, 75, 87, 91, 99, 111, 115, 119, 127, 131, 151, 155, 159, 167, 171, 175, 179, 187, 195, 207, 211, 231, 235, 239, 255, 259, 267, 279, 287, 295, 299, 307, 311, 319, 327, 335, 339, 347, 371, 375, 379, 391

Offset: 1

Jud McCranie

nonn

Related to hyperperfect numbers of a certain form.

The formula by Jaroslav Krizek is explained as follows: If p = (3n+1)/2 is prime, then it is an integer, and p must be of the form p = 3m-1, i.e., p = A003627(k). On the other hand, if p = A003627(k), then all k < p are coprime to p, so we have B(p) = (Sum_{kM. F. Hasler, Nov 29 2010

			a(6) = 19 because for A003627(6) = 29, B(29) = A053818(29)/A023896(29) = 7714/406 = 19. Cf. A179871-A179891, A003627, A007645. - _Jaroslav Krizek_, Aug 01 2010

Amiram Eldar, Table of n, a(n) for n = 1..10000
Judson S. McCranie, A study of hyperperfect numbers, J. Int. Seq., Vol. 3 (2000), Article 00.1.3.

Cf. A003627, A007645, A038536, A045309, A175505, A179871-A179891.

[ n: n in [1..400 by 2] | IsPrime((3*n+1) div 2) ];

Select[Range[500], PrimeQ[(3# + 1)/2] &] (* Harvey P. Dale, Jan 15 2011 *)

is(n)=isprime((3*n+1)/2) \\ Charles R Greathouse IV, Feb 20 2017

a(n) = A175505(A003627(n)). - Jaroslav Krizek, Aug 01 2010

Corrected by Vincenzo Librandi, Mar 24 2010

A034937 Primes p of the form 6k-1 such that 2*p + 3 is prime.

Original entry on oeis.org

5, 17, 29, 47, 53, 89, 113, 137, 167, 173, 197, 227, 269, 353, 383, 467, 503, 509, 557, 563, 599, 617, 647, 659, 743, 773, 797, 809, 827, 887, 929, 1013, 1109, 1187, 1193, 1217, 1259, 1277, 1307, 1373, 1427, 1499, 1523, 1553, 1559, 1583, 1607, 1613, 1733

Offset: 1

Jud McCranie

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

J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

Cf. A038536 and A034938.

Select[Range[5,2000,6],AllTrue[{#,2#+3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 27 2019 *)

Definition corrected by Jud McCranie, Jul 26 2019

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

Original entry on oeis.org

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

cp's OEIS Frontend

A034936 Numbers k such that 3*k + 4 is prime.

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A034934 Numbers k such that (3*k + 1)/2 is prime.

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A034937 Primes p of the form 6k-1 such that 2*p + 3 is prime.

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

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