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Revision History for A001986

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Showing entries 1-10 | older changes

Let p be the n-th odd prime. Then a(n) is the least prime congruent to 3 modulo 8 such that Legendre(-a(n), q) = -1 for all odd primes q <= p.
(history; published version)

#45 by Bruno Berselli at Fri Apr 10 11:36:09 EDT 2020

STATUS

reviewed

approved

#44 by Michel Marcus at Thu Apr 09 10:30:12 EDT 2020

STATUS

proposed

reviewed

#43 by Jinyuan Wang at Thu Apr 09 10:25:24 EDT 2020

STATUS

editing

proposed

#42 by Jinyuan Wang at Thu Apr 09 10:25:01 EDT 2020

PROG

a(n) = {my(oddpn = prime(n+1)); forprime(p=3, , if ((p%248) == 19, 3, if (isok(p, oddpn), return (p)); ); ); } \\ Michel Marcus, Oct 17 2017

STATUS

proposed

editing

Discussion

Thu Apr 09

10:25

Jinyuan Wang: done,  merci

#41 by Jinyuan Wang at Thu Apr 09 02:20:31 EDT 2020

STATUS

editing

proposed

Discussion

Thu Apr 09

02:27

Michel Marcus: I am not convinced the pari script should be touched

02:28

Michel Marcus: Joerg ?  what do you think ?

03:47

Jinyuan Wang: it can be faster, no ?

05:40

Joerg Arndt: I'd leave Pari as is; is the edited version really faster?

09:51

Michel Marcus: please revert

#40 by Jinyuan Wang at Thu Apr 09 02:18:19 EDT 2020

DATA

19, 43, 43, 67, 67, 163, 163, 163, 163, 163, 163, 222643, 1333963, 1333963, 2404147, 2404147, 20950603, 51599563, 51599563, 96295483, 96295483, 146161723, 1408126003, 3341091163, 3341091163, 3341091163, 52947440683, 52947440683, 52947440683, 193310265163

LINKS

Jinyuan Wang, <a href="/A001986/b001986.txt">Table of n, a(n) for n = 1..56</a>

PROG

(PARI) isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(-p, q) != -1, return (0)); ); return (1); }

a(n) = {my(oddpn = prime(n+1)); forprime(p=3, , if ((p%824) == 3, 19, if (isok(p, oddpn), return (p)); ); ); } \\ Michel Marcus, Oct 17 2017

EXTENSIONS

a(28)-a(30) from Jinyuan Wang, Apr 09 2020

STATUS

approved

editing

Discussion

Thu Apr 09

02:20

Jinyuan Wang: added "(PARI)". and Jianing said a(n) == 19 (mod 24),  so (p%8) == 3 -> (p%24) == 19

#39 by Peter Luschny at Thu Feb 21 15:11:05 EST 2019

STATUS

proposed

approved

#38 by Jianing Song at Tue Feb 19 07:35:47 EST 2019

STATUS

editing

proposed

#37 by Jianing Song at Tue Feb 19 07:35:37 EST 2019

COMMENTS

Also a(n) is the least prime p r congruent to 3 mod 8 such that the first n odd primes are quadratic nonresidues modulo pr. Note that p r == 3 (mod 8) implies 2 is a quadratic nonresidue modulo pr. See A001992 for the case where p r == 5 (mod 8). - Jianing Song, Feb 19 2019

CROSSREFS

Cf. A001992 (the p == congruent to 5 (mod 8) case), A094851, A094852, A094853.

STATUS

proposed

editing

#36 by Jianing Song at Tue Feb 19 04:08:57 EST 2019

STATUS

editing

proposed