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
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..1331
Programs
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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);
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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 *) -
PARI
isok(p) = isprime(p) && (q = nextprime(p+1)) && isprime(p*q-6) && isprime(p*q+6); \\ Michel Marcus, Apr 12 2014