This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123994 #45 May 27 2018 01:38:29
%S A123994 64,57,2,2,107,203,1133,1,2,1
%N A123994 Smallest number k such that prime(n)^k is a sum of 3 consecutive primes.
%C A123994 a(13) through a(23): { 1, 2, 3, 8, 1, 4, 6, 1, 729, 5, 1 }.
%C A123994 a(12) > 5387. a(24) > 3320.
%C A123994 Smallest prime p such that p^n is equal to the sum of 3 consecutive primes is given by A122706(n).
%e A123994 a(1) does not exist because there is no power of 2 that is a sum of 3 consecutive primes.
%e A123994 prime(5)^2 = 11^2 = 121 can be written as 37+41+43, therefore a(5)=2.
%o A123994 (PARI) { A123994(n) = my(k,t1,t2,t3,m); k=0; while(1, k++; m=prime(n)^k; t1=precprime(m/3); t2=nextprime(m/3); t3=m-t1-t2; if( ispseudoprime(t3) && ( (t3<t1 && t3==precprime(t1-1)) || (t3>t2 && t3==nextprime(t2+1)) ), return(k)); ); }
%Y A123994 Cf. A122706.
%K A123994 hard,more,nonn
%O A123994 2,1
%A A123994 _Alexander Adamchuk_, Oct 31 2006, Nov 02 2006
%E A123994 Corrected by _R. J. Mathar_, Jan 13 2007
%E A123994 a(8)-a(11) from _Max Alekseyev_, Apr 24 2010