A198096 n such that d(1)*1! + d(2)*2! + ... + d(k)*k! is prime, where d(i) are the decimal digits of n.

2, 3, 5, 7, 11, 12, 13, 15, 16, 18, 19, 20, 30, 31, 32, 34, 35, 37, 38, 50, 51, 53, 54, 56, 57, 59, 70, 72, 73, 75, 76, 78, 91, 92, 94, 95, 97, 101, 102, 103, 105, 106, 107, 110, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 139

Offset

1,1

Links

Table of n, a(n) for n=1..60.

Example

139 is in the sequence because 1*1! + 3*2! + 9*3! = 1 + 6 + 54 = 61 is prime.

Maple

for n from 1 to 140 do :l:=length(n):n0:=n:s:=0:for m from l by -1  to 1 do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+u*m!:od: if type(s, prime)=true then  printf(`%d, `, n):else fi:od:

Mathematica

Select[Range[200], PrimeQ[Total[IntegerDigits[#]Range[IntegerLength[#]]!]]&] (* Harvey P. Dale, Apr 12 2023 *)

Prog

(PARI) is_A198096(n)=isprime(sum(k=1, #n=Vecsmall(Str(n)), (n[k]-48)*k!)) \\ M. F. Hasler, Jan 26 2012

Crossrefs

Cf. A198044.

Sequence in context: A242694 A117288 A117283 * A137923 A163753 A131930

Adjacent sequences: A198093 A198094 A198095 * A198097 A198098 A198099

Keyword

nonn,base

Author

Michel Lagneau, Oct 21 2011

Status

approved