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a(n) = smallest integer m such that m^n is a sum of two successive primes.
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%I #26 Nov 10 2014 06:17:56

%S 5,6,2,150,22,82,2,258,70,30,42,18,2,12,262,58,460,36,552,24,318,344,

%T 450,54,274,88,36,92,90,188,554,20,404,700,240,6,136,262,578,222,2182,

%U 276,162,60,142,326,176,198,930,1116

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

%H Zak Seidov, <a href="/A226533/b226533.txt">Table of n, a(n) for n = 1..150</a>

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

%t 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 *)

%t 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 *)

%o (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

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

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 09 2013

%E a(41)-a(50) from _Jean-François Alcover_, Jun 10 2013