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 A124151 #11 Jul 23 2024 14:51:55
%S A124151 1,1,2,1,2,1,10,2,2,1,2,1,48,182,2,1,60,1,10,42,2,1,102,12,4,12,110,1,
%T A124151 12,1,100,5,28,18,144,1,102,9,2,1,30,1,186,110,130,1,566,23,1234,2,12,
%U A124151 1,336,103,142,341,1104,1,444,1,22,119,2,45,14,1,84,23,238,1,936,1,78,12
%N A124151 Smallest k such that 1 + Sum{j=1..n} k^(2*j-1) is prime.
%C A124151 a(n) = 1 if and only if n is in A006093 (primes minus 1), so 1 occurs infinitely often.
%e A124151 Consider n = 7. 1 + Sum{j=1...7} k^(2*j-1) evaluates to 8, 10923, 1793614, 71582789, 1271565756, 13433856703, 98907531458, 558482096649, 2573639151184, 10101010101011 for k = 1, ..., 10. Only the last of these numbers, 1+10+10^3+10^5+10^7+10^9+10^11+10^13 = 10101010101011, is prime, hence a(7) = 10.
%t A124151 f[n_] := Block[{k = 1}, While[ !PrimeQ[Sum[k^(2j - 1), {j, n}] + 1], k++ ]; k]; Array[f, 74] (* _Robert G. Wilson v_, Dec 17 2006 *)
%o A124151 (PARI) a(n)={my(k=1);while(!isprime(1+sum(j=1,n,k^(2*j-1))),k++); k} \\ _Klaus Brockhaus_, Dec 16 2006
%Y A124151 Cf. A006093, A124205-A124209, A124164, A124178, A124181, A124185-A124187, A124189, A124200, A124154, A124163.
%K A124151 nonn
%O A124151 1,3
%A A124151 _Artur Jasinski_, Dec 13 2006, Dec 14 2006
%E A124151 Edited and extended by _Klaus Brockhaus_, Dec 16 2006