|
%I #12 Jul 07 2023 09:33:13
%S 2,2,2,3,7,3,3,7,7,3,3,3,3,5,13,31,127,727,31,127,241,727,45361,45361,
%T 5,5,5,5,13,31,127,727,13,31,127,727,13,13,31,31,127,127,727,727,31,
%U 31,31,31,127,241,127,241,127,127,241,241,727,727,727,727,45361,45361,45361
%N Primes from integers by taking the factorial of each digit and adding them up.
%C The integers are considered in increasing order.
%C All primes eventually appear. Least integer k which produces the n-th prime: 2, 12, 122, 13, 1223, 133, 12233, 1333, 122333, 1224, 134, 1334, 122334, 13334, 1223334, ..., . - _Robert G. Wilson v_, Sep 30 2009
%H Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>
%e 2 from 11 by 1! + 1!.
%e 3 from 100 by 1! + 0! + 0!
%e 13 from 133 by 1! + 3! + 3!
%e 727 from 136 by 1! + 3! + 6!
%e 45361 from 178 by 1! + 7! + 8!
%e 155->241. 178->45361. 1223->11. 1224->29. 1333->19. 1334->37. 1336->733. 1345->151. - _R. J. Mathar_, Sep 17 2009
%t f[n_] := Plus @@ (IntegerDigits@ n!); k = 0; lst = {}; While[k < 783, a = f@k; If[ PrimeQ@a, AppendTo[lst, a]]; k++ ]; lst (* _Robert G. Wilson v_, Sep 30 2009 *)
%Y Cf. A061602. - _R. J. Mathar_, Sep 17 2009
%K base,nonn
%O 1,1
%A _Parthasarathy Nambi_, Sep 07 2009
%E 2! = 2 and 10 -> 1! + 0! = 2 prepended by _R. J. Mathar_, Sep 17 2009
|
