

A146968


Brocard's problem: positive integers n such that n!+1 = m^2.


11




OFFSET

1,1


COMMENTS

No other terms below 10^9.
See A085692 for more comments and references.  M. F. Hasler, Nov 20 2018


LINKS

Table of n, a(n) for n=1..3.
Berndt, B. C. and Galway, W. F. On the BrocardRamanujan Diophantine Equation n!+1=m^2, The Ramanujan Journal, March 2000, Volume 4, Issue 1, pp 4142.
Apoloniusz Tyszka, On sets X subset of N for which we know an algorithm that computes a threshold number t(X) in N such that X is infinite if and only if X contains an element greater than t(X), 2019.
Eric Weisstein's World of Mathematics, Brocard's Problem.


EXAMPLE

7! + 1 = 5041 = 71^2, hence 7 is in the sequence.  Klaus Brockhaus, Nov 05 2008


MATHEMATICA

Select[Range[10], IntegerQ[Sqrt[#!+1]]&] (* Harvey P. Dale, Jan 31 2015 *)


PROG

(Shell) #!/bin/sh n=0 while(true) do n=`echo $n + 1  bc` calc "($n! + 1)" ^ "(1 / 2)"  grep v \. done
(MAGMA) [ <n, p>: n in [1..8047]  t where t, p:=IsSquare(Factorial(n)+1) ]; // Klaus Brockhaus, Nov 05 2008
(PARI) { for (n=1, 60100, if(issquare(n!+1) == 1, print(n) ) ) } \\ Marco Bellaccini (marcomurk(AT)tele2.it), Nov 08 2008


CROSSREFS

A085692, A146968, A216071 are all essentially the same sequence.  N. J. A. Sloane, Sep 01 2012
Sequence in context: A095212 A166042 A321772 * A298982 A112247 A319260
Adjacent sequences: A146965 A146966 A146967 * A146969 A146970 A146971


KEYWORD

bref,nonn,hard


AUTHOR

Marco Bellaccini (marcomurk(AT)tele2.it), Nov 03 2008


EXTENSIONS

Edited by Max Alekseyev, Feb 06 2010


STATUS

approved



