A240621 Primes p such that p*q + 6 and p*q - 6 are primes where p and q are consecutive primes.

5, 7, 11, 19, 23, 37, 79, 97, 307, 349, 439, 479, 503, 719, 907, 983, 991, 1061, 1069, 1109, 1597, 1609, 1621, 1867, 2111, 2609, 3301, 3371, 3851, 4129, 4211, 4639, 4999, 5119, 5471, 5683, 5779, 5867, 5939, 6563, 7951, 9337, 9461, 9551, 10061, 10181, 10273, 12251

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1331

Example

7 is in the sequence because 7*11 + 6 = 83 and 7*11 - 6 = 71 are both prime where 7 and 11 are consecutive primes.
37 is in the sequence because 37*41 + 6 = 1523 and 37*41 - 6 = 1511 are both prime where 37 and 41 are consecutive primes.

Maple

KD := proc(n) local a, b, d; a:=ithprime(n)*ithprime(n+1); b:=a+6; d:=a-6; if  isprime(b) and isprime(d) then RETURN (ithprime(n)); fi; end: seq(KD(n), n=1..5000);

Mathematica

Select[Partition[Prime[Range[1500]], 2, 1], AllTrue[Times@@#+{6, -6}, PrimeQ]&][[All, 1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 21 2017 *)

Prog

(PARI) isok(p) = isprime(p) && (q = nextprime(p+1)) && isprime(p*q-6) && isprime(p*q+6); \\ Michel Marcus, Apr 12 2014

Crossrefs

Cf. A006094, A048880, A051507, A240596.

Sequence in context: A288446 A213981 A273048 * A040127 A341215 A136086

Adjacent sequences: A240618 A240619 A240620 * A240622 A240623 A240624

Keyword

nonn

Author

K. D. Bajpai, Apr 09 2014

Status

approved