A243522 Primes p such that p^6 - p^5 + 1 and p^6 - p^5 - 1 are both primes.

31, 181, 1039, 4591, 13687, 21589, 30211, 40771, 41641, 41947, 55441, 56437, 63559, 70867, 81307, 83407, 83869, 87649, 91639, 111229, 126199, 126499, 134287, 157999, 189559, 201307, 214129, 220699, 225751, 228559, 251431, 281557, 289717, 290839, 323767, 337639

Offset

1,1

Comments

Each term in the sequence yields, by definition, a pair of twin primes. The first term 31 results in 858874531 and 858874529, which are twin primes.

Intersection of A243471 and A243472.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1785

Example

31 is prime and appears in the sequence because [31^6 -31^5 + 1 =  858874531] and [31^6 -31^5 - 1 =  858874529] are both primes.
181 is prime and appears in the sequence because [181^6 -181^5 + 1 =  34967564082181]  and [181^6 -181^5 - 1 =  34967564082179] are both primes.

Maple

A243522 := proc() local a, b, d; a:=ithprime(n); b:= a^6-a^5+1; d:= a^6-a^5-1; if isprime (b)and isprime (d) then RETURN (a); fi; end: seq(A243522 (), n=1..30000);

Mathematica

c = 0; a = 2; Do[k = Prime[n]; If[PrimeQ[k^6 - k^5 + 1] && PrimeQ[k^6 - k^5 - 1], c++; Print[c, " ", k]], {n, 1, 2000000}];

Crossrefs

Cf. A000040, A001097, A001359, A006512, A238136.

Sequence in context: A145838 A373524 A373519 * A227523 A055788 A042876

Adjacent sequences: A243519 A243520 A243521 * A243523 A243524 A243525

Keyword

nonn

Author

K. D. Bajpai, Jun 06 2014

Status

approved