cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A147971 Indices of the records in the sequence of smallest positive quadratic nonresidues (A053760).

Original entry on oeis.org

1, 4, 9, 20, 64, 92, 246, 752, 1289, 2084, 3383, 31284, 271259, 618525, 1389315, 2228197, 2914847, 6857528, 7457772, 141236709, 366883983, 1034128714, 3690981956, 4965932454, 7863515482, 19824941433, 195348751601, 292557888940, 2296552237422
Offset: 1

Views

Author

Max Alekseyev, Nov 18 2008

Keywords

Comments

The corresponding primes are listed in A147970.

Crossrefs

Cf. A000229, A002223, A002224, A045535, A053760, A133435, A147969, A147970.

Formula

Positive integer n is in this sequence iff A053760(k) < A053760(n) for every k

Extensions

a(20)-a(29) from Charles R Greathouse IV, Apr 06 2012

A147970 Primes corresponding to the records in the sequence of smallest positive quadratic nonresidues (A053760).

Original entry on oeis.org

2, 7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 366791, 3818929, 9257329, 22000801, 36415991, 48473881, 120293879, 131486759, 2929911599, 7979490791, 23616331489, 89206899239, 121560956039, 196265095009, 513928659191, 5528920734431, 8402847753431, 70864718555231
Offset: 1

Views

Author

Max Alekseyev, Nov 18 2008

Keywords

Crossrefs

Cf. A000229, A002223, A002224, A045535, A053760, A133435, A147969, A147971.

Formula

Prime p=A000040(n) is in this sequence iff A053760(k) < A053760(n) for every kA000040(A147971(n))

Extensions

a(20)-a(29) from Charles R Greathouse IV, Apr 06 2012

A147972 Smallest prime p modulo which the first n primes are nonzero quadratic residues.

Original entry on oeis.org

7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 366791, 366791, 366791, 3818929, 9257329, 22000801, 36415991, 48473881, 120293879, 120293879, 131486759, 131486759, 2929911599, 2929911599, 7979490791, 23616331489, 23616331489, 89206899239, 121560956039, 196265095009, 196265095009, 513928659191, 5528920734431, 8402847753431, 8402847753431, 8402847753431, 70864718555231
Offset: 1

Views

Author

Max Alekseyev, Nov 18 2008

Keywords

Comments

The same primes without repetitions are listed in A147970.
a(n) <= min{A002223(n), A002224(n)}. What is the smallest n for which this inequality is strict?
By definition, a(n) == 1, 7 (mod 8), so a(n) = min{A002223(n), A002224(n)}. - Jianing Song, Feb 18 2019

Crossrefs

Cf. A000229, A002189, A002223, A002224, A045535, A053760, A133435, A147969, A147970, A147971.
Smallest prime p such that each of the first n primes has q q-th roots mod p: this sequence (q=2), A002225 (q=3), A002226 (q=5), A002227 (q=7), A002228 (q=11), A060363 (q=13), A060364 (q=17).

Programs

  • Mathematica
    (*version 7.0*)m=1;P=7;Lst={p};While[m<25,m++;S=Prime[Range[m]];While[MemberQ[JacobiSymbol[S,p],-1],p=NextPrime[p]];Lst=Append[Lst,P]];Lst (* Emmanuel Vantieghem, Jan 31 2012 *)
  • PARI
    t=2;forprime(p=2,1e9,forprime(q=2,t,if(kronecker(q,p)<1,next(2)));print1(p", ");t=nextprime(t+1);p--) \\ Charles R Greathouse IV, Jan 31 2012

Formula

a(n) >= min{A002189(n-1), A045535(n-1)}. - Jianing Song, Feb 18 2019

Extensions

a(23)-a(25) from Emmanuel Vantieghem, Jan 31 2012
a(26)-a(37) from Max Alekseyev, Aug 21 2015
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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