A126250 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.

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..7.

Formula

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

Example

1: 2! = 2^1.
2: 2! + 3! = 2^3.
3: 2! + 3! + 5! = 2^7.
5: 2! + 3! + 5! + 7! + 11! = 2^4 * 2495123.
6: 2! + 3! + 5! + 7! + 11! + 13! = 2^4 * 391683923.
16: 2! + 3! + 5! + 7! + 11! + 13! + 17! + 19! + 23! + 29! + 31! + 37! + 41! + 43! + 47! + 53!
= 2^4 * 267180205269915554141118596111444784297830210088558990999466998531923.

Crossrefs

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

Sequence in context: A355483 A079226 A055686 * A293027 A276353 A109628

Adjacent sequences: A126247 A126248 A126249 * A126251 A126252 A126253

Keyword

easy,fini,full,nonn

Author

Jonathan Vos Post, Dec 21 2006

Status

approved