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

1,1

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.

Links

Table of n, a(n) for n=1..60.

Formula

A172240 INTERSECT A006512.

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:

Crossrefs

Cf. A172487, A181669, A181602.

Sequence in context: A053458 A040058 A172057 * A216550 A267803 A240971

Adjacent sequences: A173173 A173174 A173175 * A173177 A173178 A173179

Keyword

nonn,easy

Author

Giovanni Teofilatto, Nov 22 2010

Extensions

Corrected by R. J. Mathar, Dec 01 2010

Status

approved