A173176 Greater twin primes in A172240.

7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609, 1621, 1669, 1699, 1723, 1789, 1873, 1879, 1933, 1951, 1999

Offset: 1

Author

Giovanni Teofilatto, Nov 22 2010

Keywords

• nonn
• easy

Comments

For a(n) > 5, first difference of the sequence is divisible by 6. (Conjectured or proved?)

Also for a(n)>5, a(n)-1 is divisible by 6, if a(n)-2 is prime p such that p+1 is divisible by 6.

Crossrefs

Cf. A172487, A181669, A181602.

Programs

Maple

isA006512 := proc(p) isprime(p) and isprime(p-2) ; end proc:
isA000430 := proc(p) if isprime(p) then true; else if issqr(p) then isprime(sqrt(p)) ; else false; end if; end if; end proc:
isA181602 := proc(p) if isprime(p) then if numtheory[bigomega](p-1) =2 and  isA000430(p+2) then true; else false; end if; else false;   end if ; end proc:
isA181669 := proc(p) isA181602(p) and (p mod 6)= 5 ; end proc:
isA172240 := proc(n) isprime(n) and not isA181669(n) ; end proc:
isA173176 := proc(n) isA172240(n) and isA006512(n) ; end proc:
for n from 2 to 2000 do if isA173176(n) then printf("%d,",n) ; end if; end do:

Formula

A172240 INTERSECT A006512.

Extensions

Corrected by R. J. Mathar, Dec 01 2010