A108257 Numbers k such that concatenating k and the sum of factorials of the digits of k produces a prime.

1, 13, 15, 30, 31, 91, 101, 110, 128, 133, 136, 138, 144, 152, 156, 166, 175, 193, 199, 203, 215, 230, 250, 260, 280, 281, 303, 304, 306, 307, 309, 315, 320, 330, 331, 340, 361, 391, 412, 508, 520, 550, 606, 651, 661, 681, 708, 712, 717, 730, 750, 751, 780

Offset

1,2

Comments

The largest prime I have found pertaining to this sequence is A109016(Fibonacci(9837)) with 2064 digits (not proved prime, only Fermat and Lucas PRP).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

193 is in the sequence because 1!+9!+3! = 362887 and 193362887 is prime.

Mathematica

Select[Range[780], PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[Total[IntegerDigits[#]!]]]]]&] (* James C. McMahon, Feb 22 2024 *)

Prog

(Python)
from math import factorial
from sympy import isprime
def ok(n):
    return isprime(int((s:=str(n))+str(sum(factorial(int(d)) for d in s))))
print([k for k in range(999) if ok(k)]) # Michael S. Branicky, Feb 22 2024

Crossrefs

Cf. A061602, A109016.

Sequence in context: A227449 A371287 A113801 * A217252 A299593 A318543

Adjacent sequences: A108254 A108255 A108256 * A108258 A108259 A108260

Keyword

base,nonn

Author

Jason Earls, Jun 18 2005

Status

approved