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%I #7 Apr 25 2018 10:13:45
%S 25,43,55,109,131,379,389,587,617,649,683,697,719,971,1013,1279,1291,
%T 1727,1735,1823,1853,2005,2059,2087,2167,2395,2399,2561,2647,2783,
%U 2957,2983
%N Numbers n such that n^0+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4+(n+5)^5+(n+6)^6+(n+7)^7+(n+8)^8+(n+9)^9+(n+10)^10+(n+11)^11+(n+12)^12+(n+13)^13 is a prime.
%H Chai Wah Wu, <a href="/A138091/b138091.txt">Table of n, a(n) for n = 1..1618</a>
%t a={};Do[If[PrimeQ[n^70+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4+(n+5)^5+(n+6)^6+(n+7)^7+(n+8)^8+(n+9)^9+(n+10)^10+(n+11)^11+(n+12)^12+(n+13)^13],AppendTo[a,n]],{n,10^3*3}];a
%t Select[Range[3000],PrimeQ[Total[Range[#,#+13]^Range[0,13]]]&] (* _Harvey P. Dale_, Apr 25 2018 *)
%o (Python)
%o from sympy import isprime
%o A138091_list, m = [], [6227020800, 44068147200, 181142438400, 564307430400, 1475073815040, 3408641107200, 7182564530400, 14081919023520, 26048741640120, 45924510262992, 77755456075656, 127171611204708, 201851662963039, 312086923782438]
%o for n in range(1,2*10**5+1):
%o ....for i in range(13):
%o ........m[i+1]+= m[i]
%o ....if isprime(m[-1]):
%o ........A138091_list.append(n) # _Chai Wah Wu_, Nov 06 2014
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 06 2008
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