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

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

1,1

Comments

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.

References

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

Links

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

Formula

A023242 INTERSECT A023246.

Example

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).

Mathematica

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

Prog

(Magma) [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

Crossrefs

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

Sequence in context: A196139 A165784 A329006 * A230379 A292847 A088270

Adjacent sequences: A176616 A176617 A176618 * A176620 A176621 A176622

Keyword

nonn

Author

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

Status

approved