A166980 The smallest prime p larger than prime(n) such that prime(n) is a quadratic residue (mod p).

7, 11, 11, 19, 19, 17, 19, 31, 29, 53, 41, 41, 43, 53, 53, 59, 67, 73, 73, 73, 79, 89, 103, 97, 101, 107, 127, 127, 113, 127, 139, 139, 139, 151, 173, 163, 167, 173, 173, 179, 193, 193, 193, 197, 223, 211, 223, 241, 251, 233, 241, 241, 251, 283, 283, 269, 283, 281, 281

Offset

1,1

Comments

Positions where a(n) = a(n+1) = a(n+2) = a(n+3) are for example n=737 and n=1262. - R. J. Mathar, Nov 17 2009

Links

Table of n, a(n) for n=1..59.

Example

When n=4, prime(4) = 7, and a(4) is the smallest prime above 7 with quadratic residue 7.
This yields a(4)= 19 because 8^2 = 7 (mod 19) and 19 > 7. The intermediate candidates 11, 13 and 17 fail the test.

Maple

A166980 := proc(n) local p, q, i ; q := ithprime(n) ; for i from 1 do p := ithprime(i) ; if numtheory[legendre](q, p) = 1 and p>q then return p; end if; od: end proc;
seq(A166980(n), n=1..80) ; # R. J. Mathar, Nov 02 2009

Prog

(PARI) A166980(n) = { local(q=prime(n), p=nextprime(q+1)) ; while( kronecker(q, p)!=1, p=nextprime(p+1) ; ) ; return(p) ; } { print(vector(80, n, A166980(n))); } /* R. J. Mathar, Nov 02 2009 */

Crossrefs

Sequence in context: A134702 A053674 A205679 * A184071 A243885 A171017

Adjacent sequences: A166977 A166978 A166979 * A166981 A166982 A166983

Keyword

easy,nonn

Author

J. M. Bergot, Oct 26 2009

Extensions

Some values corrected and definition clarified by R. J. Mathar, Nov 02 2009

Status

approved