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 A235392 #7 Mar 07 2019 19:44:26 %S A235392 43,157,19183,22651,37057,121453,7923366007441921, %T A235392 4496830293424385744456428801,45045561823582321,412807, %U A235392 49907098805169447878401,34672666242568358583785606401,1041421 %N A235392 Primes of the form (p! + q!)/ p! where p= prime(k) and q= prime(k+1), in order of increasing k. %C A235392 The 6th term has 6 digits; the 44th term has 44 digits. %C A235392 The 685th term has 349 digits. %H A235392 K. D. Bajpai, <a href="/A235392/b235392.txt">Table of n, a(n) for n = 1..1000</a> %e A235392 43 is in the sequence because (5! + 7!)/ 5! = (120 + 5040)/120 = 43 which is prime and 5 and 7 are consecutive primes. %e A235392 157 is in the sequence because (11! + 13!)/ 11! = (39916800 + 6227020800)/ 39916800 = 157 which is prime and 11 and 13 are consecutive primes. %p A235392 KD := proc() local a,b,d; a:=ithprime(n); b:=ithprime(n+1); d:=(a! + b!)/ a!; if isprime(d) then RETURN (d); fi; end: seq(KD(), n=1..300); %t A235392 Select[((#[[1]]!+#[[2]]!)/#[[1]]!&/@Partition[Prime[Range[ 300]], 2,1]), PrimeQ] (* _Harvey P. Dale_, Mar 07 2019 *) %Y A235392 Cf. A000040 (prime numbers). %Y A235392 Cf. A100858 (primes:(p-1)! + p). %K A235392 nonn %O A235392 1,1 %A A235392 _K. D. Bajpai_, Jan 09 2014