

A257231


a(n) = n^2 mod p where p is the least prime greater than n.


2



1, 1, 4, 1, 4, 1, 5, 9, 4, 1, 4, 1, 16, 9, 4, 1, 4, 1, 16, 9, 4, 1, 7, 25, 16, 9, 4, 1, 4, 1, 36, 25, 16, 9, 4, 1, 16, 9, 4, 1, 4, 1, 16, 9, 4, 1, 36, 25, 16, 9, 4, 1, 36, 25, 16, 9, 4, 1, 4, 1, 36, 25, 16, 9, 4, 1, 16, 9, 4, 1, 4, 1, 36, 25, 16, 9, 4, 1, 16, 9, 4, 1, 36, 25, 16, 9, 4
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OFFSET

1,3


COMMENTS

Conjecture: a(n) is always a positive square, except for the terms 5, 7, 69, 42 and 17 given by n = 7, 23, 113, 114, and 115 respectively. It is easy to show that nonsquare terms are in [p, q) iff p and q are consecutive primes and qp > sqrt(q). There are no gaps between consecutive primes greater than sqrt(q) for 127 < q < 4*10^18 (see Nicely's table of maximal prime gaps).


LINKS



EXAMPLE

a(23) = 7 because 23^2 mod 29 = 7.
a(24) = 25 because 24^2 mod 29 = 25.


MATHEMATICA

Table[PowerMod[n, 2, NextPrime[n]], {n, 90}] (* Harvey P. Dale, May 24 2015 *)


PROG

(PARI) a(n)=n^2%nextprime(n+1)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



