Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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