A126250 - OEIS

%I #6 Jun 24 2014 14:41:33

%S 1,2,3,5,6,16,27

%N Numbers n such that the sum of the first n factorials of primes is either a power of 2 or a prime times a power of 2.

%C Note that from 2!+3!+5!+7! on, the power of 2 will always be 2^4. So after the first 3 terms, an equivalent definition is that the sum has the form 16p for some prime p. Also, the sequence is finite: For all n>=762, prime(1)! + ... + prime(n)! is divisible by prime(763) = 5813 and is therefore not of the form 16p. - _Dean Hickerson_.

%F n such that SUM[i=1..n] p(i)! is in A093641.

%e 1: 2! = 2^1.

%e 2: 2! + 3! = 2^3.

%e 3: 2! + 3! + 5! = 2^7.

%e 5: 2! + 3! + 5! + 7! + 11! = 2^4 * 2495123.

%e 6: 2! + 3! + 5! + 7! + 11! + 13! = 2^4 * 391683923.

%e 16: 2! + 3! + 5! + 7! + 11! + 13! + 17! + 19! + 23! + 29! + 31! + 37! + 41! + 43! + 47! + 53!

%e = 2^4 * 267180205269915554141118596111444784297830210088558990999466998531923.

%Y Cf. A000040, A000142, A059590, A074257, A093641, A101548, A114333, A114337, A114339, A122990.

%K easy,fini,full,nonn

%O 1,2

%A _Jonathan Vos Post_, Dec 21 2006