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 A342690 #45 Jul 10 2021 17:46:48 %S A342690 2,3,5,8,17,27,41,59,71,89,101,131,167,173,293,383,512,677,701,743, %T A342690 761,773,827,839,857,911,1091,1097,1163,1181,1193,1217,1331,1373,1427, %U A342690 1487,1559,1583,1709,1811,1847,1931,1973,2129,2273,2309,2339,2411,2663 %N A342690 Prime powers q in A246655 such that q^2 + q + 1 is prime. %C A342690 Also, prime powers q = p^(3^k) with prime p and nonnegative integer k and the property that q^2 + q + 1 is prime, since the exponent must be a power of 3, from the theory of cyclotomic polynomials. 17^(3^7) is in the sequence, generating a 5382-digit prime. %H A342690 Martin Becker, <a href="/A342690/b342690.txt">Table of n, a(n) for n = 1..20000</a> %e A342690 5 = 5^1 is a term: 5^2 + 5 + 1 = 31 is prime. %e A342690 8 = 2^3 is a term: 8^2 + 8 + 1 = 73 is prime. %t A342690 Select[Range@2000,PrimePowerQ@#&&PrimeQ[#^2+#+1]&] (* _Giorgos Kalogeropoulos_, May 18 2021 *) %o A342690 (PARI) N=50; i=0; a=vector(N); for(q=2, oo, if(isprimepower(q) && isprime(q^2+q+1), i+=1; a[i]=q; if(i==N, break))); a %Y A342690 Intersection of A246655 and A002384. %Y A342690 Cf. A342691, A344448. %K A342690 nonn %O A342690 1,1 %A A342690 _Martin Becker_, May 18 2021