The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A275777

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A275777

Primes p such that there are exactly p solutions to y^2 + x*y + y == x^3 + x^2 - 10*x - 10 (mod p).
(history; published version)

#40 by Bruno Berselli at Mon Sep 12 10:55:02 EDT 2016

STATUS

reviewed

approved

#39 by Joerg Arndt at Mon Sep 12 09:34:42 EDT 2016

STATUS

proposed

reviewed

#38 by Charles R Greathouse IV at Mon Sep 12 09:25:06 EDT 2016

STATUS

editing

proposed

#37 by Charles R Greathouse IV at Mon Sep 12 09:21:54 EDT 2016

PROG

(PARI) \\ Much slower than the above, but maybe useful for isolated values

is(n)=if(!isprime(n), return(0)); my(s, t, y='y); for(x=1, n, s+=#polrootsmod(y^2+x*y+y-x^3-x^2+10*x+10, n); if(s>n, return(0))); s==n \\ Charles R Greathouse IV, Sep 12 2016

#36 by Charles R Greathouse IV at Sun Sep 11 14:27:24 EDT 2016

NAME

Primes for which A275742(n) p such that there are exactly p solutions to y^2 + x*y + y == primex^3 + x^2 - 10*x - 10 (nmod p).

COMMENTS

Primes p = prime(n) for which A275742(n) = p.

These terms are the primes Primes p for which A030184(p) == 0 (mod p).

These terms are the primes Primes prime(A275745(n)) for which A275745(n) = 0.

STATUS

approved

editing

#35 by Joerg Arndt at Sun Sep 11 02:13:01 EDT 2016

STATUS

proposed

approved

#34 by Joerg Arndt at Sun Sep 11 02:11:56 EDT 2016

STATUS

editing

proposed

Discussion

Sun Sep 11

02:13

Seiichi Manyama: Sorry, My code is too slow, as you know.

#33 by Joerg Arndt at Sun Sep 11 02:11:48 EDT 2016

PROG

(PARI)

#32 by Joerg Arndt at Sun Sep 11 02:11:04 EDT 2016

DATA

7, 23, 31, 79, 167, 431, 479, 983, 1303, 1607, 1871, 2351, 4799, 6263, 6271, 9551, 10103, 10111, 11471, 11519, 12503, 12647, 12959, 14087, 17231, 17623, 21599, 23039, 25391, 25919, 25951, 28879, 29927, 33599, 35543, 43711, 48479, 48647, 49871, 56671, 57119, 62743, 71551, 71999, 79151, 81551, 82567, 91703, 96079, 97919

PROG

{ N = 10^5 + 2;

default(seriesprecision, N);

V = Vec( eta(q) * eta(q^3) * eta(q^5) * eta(q^15) );

forprime(p=2, N, if( V[p]%p == 0, print1(p, ", ") ) );

} \\ Joerg Arndt, Sep 11 2016

KEYWORD

nonn,more,new

EXTENSIONS

More terms from Joerg Arndt, Sep 11 2016

STATUS

proposed

editing

Discussion

Sun Sep 11

02:11

Joerg Arndt: All terms <= 10^5.  Now you can compute a b-file if you like.

#31 by Michel Marcus at Sun Sep 11 00:21:11 EDT 2016

STATUS

editing

proposed