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A227644
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Perfect powers equal to the sum of 2 factorial numbers.
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10
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OFFSET
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1,1
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COMMENTS
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a(7), if it exists, is greater than 10^100.
a(7), if it exists, is greater than 10000!. - Filip Zaludek, Jul 18 2017
a(7), if it exists, is greater than 11750!. - Filip Zaludek, Sep 07 2018
a(7), if it exists, is greater than 20000!. - Filip Zaludek, Nov 04 2020
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LINKS
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EXAMPLE
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5041 = 71^2 = 1! + 7!.
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PROG
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(C)
#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>
int main()
{
int bsz=256, a=0;
mpz_t *f, t;
f = malloc(sizeof(mpz_t) * bsz);
mpz_init(t); mpz_init(f[0]); mpz_set_ui(f[0], 1);
while (1)
{
a += 1;
if (a == bsz)
{
bsz *= 2;
f = (mpz_t *) realloc(f, sizeof(mpz_t) * bsz);
}
mpz_init(f[a]);
mpz_mul_ui(f[a], f[a-1], a);
for (int i=1; i<=a; i++)
{
mpz_add(t, f[a], f[i]);
if (mpz_perfect_power_p(t))
{
gmp_printf("%Zd, ", t);
fflush(stdout);
}
}
}
return 0;
}
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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