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%I #13 Jun 06 2014 11:17:17
%S 3,97,367,397,409,457,487,499,691,709,727,751,769,919,937,991,1117,
%T 1171,1201,1381,1447,1531,1567,1579,1741,1831,1987,2011,2161,2221,
%U 2251,2281,2467,2539,2617,2671,2707,2749,2851,2887,2917,3019,3049,3217,3229,3457,3499
%N Larger of the two consecutive primes whose positive difference is a cube.
%C Observation: All the terms in this sequence, after a(1), are the larger of the two consecutive primes which have positive difference either 2^3 or 4^3.
%C Superset of A031927 as the sequence contains for example numbers like 89753, 107441, 288647,.. (with gaps of 4^3...) that are not in A031927. - _R. J. Mathar_, Jun 06 2014
%H K. D. Bajpai, <a href="/A243155/b243155.txt">Table of n, a(n) for n = 1..10000</a>
%e 97 is prime and appears in the sequence because 97 - 89 = 8 = 2^3.
%e 397 is prime and appears in the sequence because 397 - 389 = 8 = 2^3.
%p A243155:= proc() local a; a:=evalf((ithprime(n+1)-ithprime(n))^(1/3)); if a=floor(a) then RETURN (ithprime(n+1)); fi; end: seq(A243155 (), n=1..100);
%t n = 0; Do[t = Prime[k] - Prime[k - 1]; If[IntegerQ[t^(1/3)], n++; Print[n, " ", Prime[k]]], {k, 2, 15*10^4}]
%o (PARI) s=[]; forprime(p=3, 4000, if(ispower(p-precprime(p-1), 3), s=concat(s, p))); s \\ _Colin Barker_, Jun 03 2014
%Y Cf. A031927, A123996, A118590, A001632.
%K nonn
%O 1,1
%A _K. D. Bajpai_, May 31 2014
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