

A243155


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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


LINKS

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


EXAMPLE

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.


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}]


PROG

(PARI) s=[]; forprime(p=3, 4000, if(ispower(pprecprime(p1), 3), s=concat(s, p))); s \\ Colin Barker, Jun 03 2014


CROSSREFS

Cf. A031927, A123996, A118590, A001632.
Sequence in context: A209554 A320513 A320517 * A201843 A278202 A246537
Adjacent sequences: A243152 A243153 A243154 * A243156 A243157 A243158


KEYWORD

nonn


AUTHOR

K. D. Bajpai, May 31 2014


STATUS

approved



