A235392 Primes of the form (p! + q!)/ p! where p= prime(k) and q= prime(k+1), in order of increasing k.

43, 157, 19183, 22651, 37057, 121453, 7923366007441921, 4496830293424385744456428801, 45045561823582321, 412807, 49907098805169447878401, 34672666242568358583785606401, 1041421

Offset: 1

Author

K. D. Bajpai, Jan 09 2014

Keywords

• nonn

Comments

The 6th term has 6 digits; the 44th term has 44 digits.

The 685th term has 349 digits.

Examples

			43 is in the sequence because (5! + 7!)/ 5! = (120 + 5040)/120 = 43 which is prime and 5 and 7 are consecutive primes.
157 is in the sequence because (11! + 13!)/ 11! = (39916800 + 6227020800)/ 39916800 = 157 which is prime and 11 and 13 are consecutive primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040 (prime numbers).

Cf. A100858 (primes:(p-1)! + p).

Programs

Maple

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);

Mathematica

Select[((#[[1]]!+#[[2]]!)/#[[1]]!&/@Partition[Prime[Range[ 300]], 2,1]), PrimeQ] (* Harvey P. Dale, Mar 07 2019 *)