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 A368749 #18 Jan 20 2024 09:38:04
%S A368749 2,5,13,19,31,53,359,89,241,139,509,113,839,293,2803,1831,523,1069,
%T A368749 11447,887,3469,1129,1669,4177,39581,2477,24631,2971,16381,4297,
%U A368749 124601,5591,1327,8467,22193,9551,79493,30593,62989,19333,410857,16141,436913,15683,1038337,81463,157579
%N A368749 a(n) is the smallest prime p such that there are n numbers between p and nextprime(p) which are not prime powers.
%C A368749 Conjecture: the sequence is infinite (number of nonprime powers between consecutive primes is arbitrarily large; see A014963).
%e A368749 a(2) = 13 because between 13 and 17 there are three composite numbers, only one of which (16) is a prime power, and no previous prime has this property.
%e A368749 a(5) = 53 because between 53 and 59 there are 5 composite numbers, none of which are prime powers, and no smaller prime has this property.
%t A368749 p = q = 2; r = a[_] = 0; Do[q = NextPrime[q]; If[a[#] == 0, a[#] = p; If[# > r, r = #]] &@ Count[Range[p, q - 1], _?(Not@*PrimePowerQ)]; p = q, {i, 2^16}]; {2}~Join~TakeWhile[Array[a, r], # > 0 &] (* _Michael De Vlieger_, Jan 04 2024 *)
%o A368749 (PARI) f(p) = sum(k=p+1, nextprime(p+1)-1, !isprimepower(k));
%o A368749 a(n) = my(p=2); while(f(p) != n, p=nextprime(p+1)); p; \\ _Michel Marcus_, Jan 04 2024
%Y A368749 Cf. A000040, A000230, A000961, A014963, A024619, A080101, A085970, A093555, A368748.
%K A368749 nonn
%O A368749 0,1
%A A368749 _David James Sycamore_ and _Michael De Vlieger_, Jan 04 2024
%E A368749 More terms from _Michel Marcus_, Jan 04 2024