A226533 a(n) = smallest integer m such that m^n is a sum of two successive primes.

5, 6, 2, 150, 22, 82, 2, 258, 70, 30, 42, 18, 2, 12, 262, 58, 460, 36, 552, 24, 318, 344, 450, 54, 274, 88, 36, 92, 90, 188, 554, 20, 404, 700, 240, 6, 136, 262, 578, 222, 2182, 276, 162, 60, 142, 326, 176, 198, 930, 1116

Offset: 1

Author

Zak Seidov, Jun 09 2013

Keywords

• nonn

Examples

			5^1 = 5 = 2 + 3, 6^2 = 36  = 17 + 19, 2^3 = 8 = 3 + 5, 150^4 =506250000 = 253124999 + 253125001.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..150

Crossrefs

a(2) = 6 = A074924(1), a(3) = 2 = A074925(1). Cf. A001043, A001597.

Programs

Mathematica

a[n_] := For[m = 2, True, m++, p = m^n/2 // NextPrime[#, -1]&; q = NextPrime[p]; If[p + q == m^n, Print["a(", n, ") = ", m]; Return[m]]]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jun 10 2013 *)
tsp[n_]:=Module[{m=1,t},t=m^n;While[NextPrime[t/2]+NextPrime[t/2, -1]! = t,m++;t=m^n];m]; Array[tsp,50] (* Harvey P. Dale, Nov 10 2014 *)

PARI

a(n)=if(n==1,return(5)); my(m=1,M,p); while(1,M=m++^n;p=precprime(M/2); ispseudoprime(M-p) && M-p==nextprime(M/2) && return(m)) \\ Charles R Greathouse IV, Jun 10 2013

Extensions

a(41)-a(50) from Jean-François Alcover, Jun 10 2013