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A379760 Smallest prime that is the sum of 2n+1 cubes of consecutive odd primes.

%I A379760 #43 Feb 03 2025 02:24:13
%S A379760 66347,15643,81647,279397,1961623,3701627,5644601,2505187,8016551,
%T A379760 4695947,9335519,6819443,12830327,35259463,35278489,56759723,39944393,
%U A379760 86442623,186387137,95860493,118647143,170943137,118651139,509399153,241399309,381448853,877324879
%N A379760 Smallest prime that is the sum of 2n+1 cubes of consecutive odd primes.
%H A379760 Robert Israel, <a href="/A379760/b379760.txt">Table of n, a(n) for n = 1..10000</a>
%e A379760 For n=2, the smallest sum of 2*n+1 = 5 cubed consecutive primes which is prime is a(2) = 7^3 + 11^3 + 13^3 + 17^3 + 19^3 = 15643.
%p A379760 P3:= map(t -> t^3, select(isprime,[seq(i,i=3..10^5,2)])):
%p A379760 SP3:= ListTools:-PartialSums(P3):
%p A379760 f:= proc(n) local k;
%p A379760   for k from 1 do if isprime(SP3[k+2*n+1]-SP3[k]) then return SP3[k+2*n+1]-SP3[k] fi od
%p A379760 end proc:
%p A379760 map(f, [$1..50]); # _Robert Israel_, Feb 02 2025
%t A379760 a[n_] := Block[{k = 1, s}, While[s = Sum[Prime[i]^3, {i, k, k + 2n}]; !PrimeQ[s], k++ ]; s]; Table[a[n], {n, 1, 27}]
%o A379760 (PARI) a(n) = my(k=2, s = sum(i=0, 2*n, prime(k+i)^3)); while (!isprime(s), s -= prime(k)^3; k++; s += prime(k+2*n)^3;); s; \\ _Michel Marcus_, Jan 20 2025
%Y A379760 Cf. A030078 (cube of primes), A082244 (analog for primes), A380319 (analog for square of primes).
%K A379760 nonn
%O A379760 1,1
%A A379760 _Michel Lagneau_, Jan 02 2025