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 A291554 #33 Aug 31 2017 16:46:45 %S A291554 31,73,89,109,113,127,151,157,193,233,241,257,281,307,313,331,337,353, %T A291554 397,433,457,499,577,593,601,641,673,683,811,919,953,1013,1049,1103, %U A291554 1153,1163,1201,1217,1249,1321,1327,1399,1429,1433,1459,1471,1553,1601,1613,1657,1709,1721,1753,1777,1789,1801,1873,1913,1933,1993 %N A291554 Primes q for which there exists a prime p < q such that 2^q == 2^p (mod pq). %C A291554 Largest prime divisors of pseudoprimes with two distinct prime factors. %C A291554 All prime divisors of pseudoprimes with two prime factors are all primes except 2, 3, 5, 7, and 13. %H A291554 Charles R Greathouse IV, <a href="/A291554/b291554.txt">Table of n, a(n) for n = 1..10000</a> %F A291554 Equivalent congruences: 2^(pq) == 2 (mod pq), 2^q == 2^p == 2 (mod pq), 2^(q-p) == 1 (mod pq), 2^gcd(p-1,q-1) == 1 (mod pq). %e A291554 We have 2^31 == 2^11 == 2 (mod 11*31), so 31 is a term. %e A291554 Note that 11*31 = 341 is a pseudoprime. %t A291554 Select[Prime@ Range[300], Function[p, AnyTrue[Prime@ Range[PrimePi[p] - 1], Function[q, PowerMod[2, q, p q] == PowerMod[2, p, p q]]]]] (* _Michael De Vlieger_, Aug 27 2017 *) %o A291554 (PARI) is(n)=forprime(p=2,n-1, if(Mod(2,p*n)^gcd(n-1,p-1)==1, return(isprime(n)))); 0 \\ _Charles R Greathouse IV_, Aug 26 2017 %o A291554 (PARI) is(n)=if(n<9 || !isprime(n), return(0)); my(t=Mod(1,znorder(Mod(2,n))), nm1=n-1); t=chinese(t, Mod(1,2)); forstep(p=lift(t),n-2,t.mod, if(isprime(p) && Mod(2,p*n)^gcd(nm1,p-1)==1, return(1))); 0 \\ _Charles R Greathouse IV_, Aug 31 2017 %Y A291554 Cf. A001567, A214305, A216838. %K A291554 nonn %O A291554 1,1 %A A291554 _Thomas Ordowski_, Aug 26 2017 %E A291554 More terms from _Robert Israel_, Aug 26 2017