cp's OEIS Frontend

A227644 Perfect powers equal to the sum of 2 factorial numbers.

%I A227644 #23 Nov 05 2020 06:48:29
%S A227644 4,8,25,121,144,5041
%N A227644 Perfect powers equal to the sum of 2 factorial numbers.
%C A227644 a(7), if it exists, is greater than 10^100.
%C A227644 a(7), if it exists, is greater than 10000!. - _Filip Zaludek_, Jul 18 2017
%C A227644 a(7), if it exists, is greater than 11750!. - _Filip Zaludek_, Sep 07 2018
%C A227644 a(7), if it exists, is greater than 20000!. - _Filip Zaludek_, Nov 04 2020
%H A227644 Giovanni Resta, <a href="/A227644/a227644.txt">Decompositions of a(1)-a(6)</a>
%e A227644 5041 = 71^2 = 1! + 7!.
%o A227644 (C)
%o A227644 /* To compile: gcc -Wall -O2 A227644.c -o A227644 -lgmp */
%o A227644 #include <stdio.h>
%o A227644 #include <stdlib.h>
%o A227644 #include <gmp.h>
%o A227644 int main()
%o A227644 {
%o A227644    int bsz=256, a=0;
%o A227644    mpz_t *f, t;
%o A227644    f = malloc(sizeof(mpz_t) * bsz);
%o A227644    mpz_init(t); mpz_init(f[0]); mpz_set_ui(f[0], 1);
%o A227644    while (1)
%o A227644    {
%o A227644        a += 1;
%o A227644        if (a == bsz)
%o A227644        {
%o A227644            bsz *= 2;
%o A227644            f = (mpz_t *) realloc(f, sizeof(mpz_t) * bsz);
%o A227644        }
%o A227644        mpz_init(f[a]);
%o A227644        mpz_mul_ui(f[a], f[a-1], a);
%o A227644        for (int i=1; i<=a; i++)
%o A227644        {
%o A227644            mpz_add(t, f[a], f[i]);
%o A227644            if (mpz_perfect_power_p(t))
%o A227644            {
%o A227644                gmp_printf("%Zd, ", t);
%o A227644                fflush(stdout);
%o A227644            }
%o A227644        }
%o A227644    }
%o A227644    return 0;
%o A227644 }
%Y A227644 Cf. A114377, A227645, A227646, A227647, A227648, A227649, A227650, A227651, A065433, A085692.
%K A227644 nonn,more
%O A227644 1,1
%A A227644 _Giovanni Resta_, Jul 19 2013