A023246 -id:A023246 - cp's OEIS frontend

A023307 Primes that remain prime through 4 iterations of function f(x) = 3x + 2.

1129, 10009, 11489, 12539, 13859, 30029, 63079, 77359, 99119, 121039, 124669, 169409, 194749, 205589, 246329, 330329, 349519, 351829, 354839, 361279, 369539, 384589, 395719, 399769, 416989, 429109, 446819, 527599, 532489, 544259, 575119

Offset: 1

David W. Wilson

nonn

Primes p such that 3*p+2, 9*p+8, 27*p+26, and 81*p+80 are also primes. - Vincenzo Librandi, Aug 04 2010

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A023208, A023246, A023277, and A024893.

[n: n in [1..1000000] | IsPrime(n) and IsPrime(3*n+2) and IsPrime(9*n+8) and IsPrime(27*n+26) and IsPrime(81*n+80)] // Vincenzo Librandi, Aug 04 2010

Select[Prime[Range[50000]],AllTrue[Rest[NestList[3#+2&,#,4]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 13 2015 *)

a(n) == 9 or 69 (mod 70). - John Cerkan, Oct 04 2016

A176619 Primes p such that 2p + 3, 4p + 9, 3p + 2 and 9p + 8 are also primes.

Original entry on oeis.org

5, 7, 97, 167, 397, 607, 2617, 2707, 7687, 12097, 14407, 16787, 19577, 22307, 23827, 24967, 25717, 28547, 31687, 43037, 43517, 46817, 58967, 59617, 63607, 70237, 70957, 78517, 85027, 96797

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 22 2010

nonn

These primes stay prime under two iterations of p->2p+3 as well as under two iterations of p->3p+2.

For all entries >5 the least significant digit is 7.

			2*5 + 3 = 13 = prime(6),
4*5 + 9 = 29 = prime(10),
3*5 + 2 = 17 = prime(7),
9*5 + 8 = 53 = prime(16); 5 = prime(3) = a(1).

Joe Buhler: Algorithmic Number Theory: Third International Symposium, ANTS-III, Springer New York, 1998
F. Ischebeck: Einladung zur Zahlentheorie, B. I. Wissenschaftsverlag, Mannheim-Leipzig-Wien-Zuerich, 1992

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A005602, A023242, A023246, A059762.

[p: p in PrimesUpTo(100000)|IsPrime(2*p+3) and IsPrime(4*p+9) and IsPrime(3*p+2) and IsPrime(9*p+8 )] // Vincenzo Librandi, Jan 29 2011

Select[Prime[Range[10000]],AllTrue[{2#+3,4#+9,3#+2,9#+8},PrimeQ]&] (* Harvey P. Dale, Dec 15 2024 *)

A023242 INTERSECT A023246.

cp's OEIS Frontend

A023307 Primes that remain prime through 4 iterations of function f(x) = 3x + 2.

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