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 A294925 #22 Jan 15 2021 23:08:44 %S A294925 2,6,30,210,15810,292110,16893030,984016110,17088913842,2446241358990, %T A294925 1098013758964122 %N A294925 a(n) is the smallest number k with n prime factors such that p + k/p is prime for every prime p | k. %C A294925 Such k is an even squarefree number. %C A294925 Conjecture: the sequence is infinite. %e A294925 a(2) = 6 because k = 2*3 = 6 is the smallest number with 2 prime factors such that 2 + 6/2 = 3 + 6/3 = 5 is prime. %e A294925 From _Michael De Vlieger_, Nov 13 2017: (Start) %e A294925 First differences of prime indices of a(n): %e A294925 n a(n) A287352(a(n)) %e A294925 ---------------------------------------------------------- %e A294925 1 2 1 %e A294925 2 6 1, 1 %e A294925 3 30 1, 1, 1, %e A294925 4 210 1, 1, 1, 1 %e A294925 5 15810 1, 1, 1, 4, 4 %e A294925 6 292110 1, 1, 1, 1, 2, 22 %e A294925 7 16893030 1, 1, 1, 1, 1, 15, 7 %e A294925 8 984016110 1, 1, 1, 1, 1, 5, 2, 66 %e A294925 9 17088913842 1, 1, 2, 1, 1, 1, 1, 1, 67 %e A294925 10 2446241358990 1, 1, 1, 2, 1, 2, 2, 3, 1, 93 %e A294925 11 1098013758964122 1, 1, 2, 1, 1, 3, 2, 8, 3, 22, 10 %e A294925 (End) %o A294925 (PARI) isok(k, n) = {if (!issquarefree(k), return (0)); if (omega(k) != n, return (0)); fordiv(k, d, if (isprime(d) && !isprime(d+k/d), return(0));); return (1);} %o A294925 a(n) = {my(k=1); while( !isok(k, n), k++); k;} \\ _Michel Marcus_, Nov 11 2017 %Y A294925 Cf. A293756. %K A294925 nonn,more %O A294925 1,1 %A A294925 _Thomas Ordowski_, Nov 11 2017 %E A294925 a(5)-a(7) from _Michel Marcus_, Nov 11 2017 %E A294925 a(8) from _Michel Marcus_, Nov 12 2017 %E A294925 a(9)-a(10) from _Michael De Vlieger_, Nov 13 2017 %E A294925 a(11) (and update of table in Example section) from _Jon E. Schoenfield_, Nov 19 2017