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%I #15 Mar 30 2012 18:40:08
%S 7,13,19,31,43,61,73,103,109,139,151,181,193,199,229,241,271,283,313,
%T 349,421,433,463,523,571,601,619,643,661,811,823,829,859,883,1021,
%U 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
%N Greater twin primes in A172240.
%C For a(n) > 5, first difference of the sequence is divisible by 6. (Conjectured or proved?)
%C 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.
%F A172240 INTERSECT A006512.
%p isA006512 := proc(p) isprime(p) and isprime(p-2) ; end proc:
%p isA000430 := proc(p) if isprime(p) then true; else if issqr(p) then isprime(sqrt(p)) ; else false; end if; end if; end proc:
%p 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:
%p isA181669 := proc(p) isA181602(p) and (p mod 6)= 5 ; end proc:
%p isA172240 := proc(n) isprime(n) and not isA181669(n) ; end proc:
%p isA173176 := proc(n) isA172240(n) and isA006512(n) ; end proc:
%p for n from 2 to 2000 do if isA173176(n) then printf("%d,",n) ; end if; end do:
%Y Cf. A172487, A181669, A181602.
%K nonn,easy
%O 1,1
%A _Giovanni Teofilatto_, Nov 22 2010
%E Corrected by _R. J. Mathar_, Dec 01 2010
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