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Lesser of twin primes in A172240.
3

%I #10 Mar 30 2012 18:40:08

%S 3,17,29,41,71,101,137,149,191,197,239,269,281,311,419,431,461,521,

%T 569,599,617,641,659,809,821,827,857,881,1031,1049,1061,1091,1151,

%U 1229,1277,1289,1301,1427,1451,1481,1607,1667,1697,1721,1787,1871,1877,1931,1949,1997

%N Lesser of twin primes in A172240.

%C For a(n) > 3, the first differences of the sequence are divisible by 6. (Is this a conjecture or a theorem?)

%F A001359 INTERSECT A172240.

%p isA001359 := 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 isA181669 := proc(p) if isprime(p) and (p mod 6)= 5 then if numtheory[bigomega](p-1) =2 and isA000430(p+2) then true; else false; end if;else false; end if ; end proc:

%p isA172240 := proc(n) isprime(n) and not isA181669(n) ; end proc:

%p isA172487 := proc(n) isA172240(n) and isA001359(n) ; end proc:

%p for n from 2 to 2000 do if isA172487(n) then printf("%d,",n) ; end if;end do:

%Y Cf. A173176, A172240, A181669, A181602.

%K nonn,easy

%O 1,1

%A _Giovanni Teofilatto_, Nov 21 2010