A243155 Larger of the two consecutive primes whose positive difference is a cube.

3, 97, 367, 397, 409, 457, 487, 499, 691, 709, 727, 751, 769, 919, 937, 991, 1117, 1171, 1201, 1381, 1447, 1531, 1567, 1579, 1741, 1831, 1987, 2011, 2161, 2221, 2251, 2281, 2467, 2539, 2617, 2671, 2707, 2749, 2851, 2887, 2917, 3019, 3049, 3217, 3229, 3457, 3499

Offset: 1

Author

K. D. Bajpai, May 31 2014

Keywords

• nonn

Comments

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.

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

Examples

			97 is prime and appears in the sequence because 97 - 89 = 8 = 2^3.
397 is prime and appears in the sequence because 397 - 389 = 8 = 2^3.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A031927, A123996, A118590, A001632.

Programs

Maple

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);

Mathematica

n = 0; Do[t = Prime[k] - Prime[k - 1]; If[IntegerQ[t^(1/3)], n++; Print[n, " ", Prime[k]]], {k, 2, 15*10^4}]

PARI

s=[]; forprime(p=3, 4000, if(ispower(p-precprime(p-1), 3), s=concat(s, p))); s \\ Colin Barker, Jun 03 2014