A243522 - OEIS

%I #11 Jun 07 2014 02:45:31

%S 31,181,1039,4591,13687,21589,30211,40771,41641,41947,55441,56437,

%T 63559,70867,81307,83407,83869,87649,91639,111229,126199,126499,

%U 134287,157999,189559,201307,214129,220699,225751,228559,251431,281557,289717,290839,323767,337639

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

%C 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.

%C Intersection of A243471 and A243472.

%H K. D. Bajpai, <a href="/A243522/b243522.txt">Table of n, a(n) for n = 1..1785</a>

%e 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.

%e 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.

%p 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);

%t 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}];

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

%K nonn

%O 1,1

%A _K. D. Bajpai_, Jun 06 2014