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A166980 The smallest prime p larger than prime(n) such that prime(n) is a quadratic residue (mod p). 1
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 (list; graph; refs; listen; history; text; internal format)
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. [From 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

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Last modified June 28 05:07 EDT 2017. Contains 288813 sequences.