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 1-5 of 5 results.

A091381 First differences of A091380.

Original entry on oeis.org

0, 2, 1, 5, 2, 3, 3, 1, 9, 1, 7, 3, 3, 1, 9, 6, 2, 6, -1, 4, 8, 5, 5, 6, 7, 1, 5, 2, 3, 14, 5, 5, 3, 10, 1, 7, 6, 1, 9, 6, 2, 5, 4, 7, 1, 13, 11, 5, 2, 3, 2, 2, 15, 5, 4, 9, 1, 7, 3, 3, 10, 14, -5, 8, 7, 14, 3, 13, 2, 3, 2, 12, 7, 6, 1, 9, 8, 3, 4, 15, 2, 5, 4, 8, 5, 5, 6, 7, 1, 5, 1, 18, 5, 8, 1, 9, 11, 3, 18
Offset: 1

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Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

Comments

Seemingly, the difference sequence is mostly positive. There are special characteristic features, where it is nonpositive (see A091383-A091385).

Links

Crossrefs

Cf. A091380, A091382, A091383, A091384, A091385, A088191, A088197.

Programs

  • PARI
    {/* Difference sequence of the largest "mixed" QR modulo the primes */ d_lqxr(to)=local(v=[],k,r,q,p,e=1); for(i=2,to,p=prime(i);k=p-1;r=p%4-2; while(kronecker(k,p)<>r,k-=1); v=concat(v,k-e);e=k); print(v) }

A091382 Distance between the sequence of primes and the largest "mixed" quadratic residues modulo the primes (A091380).

Original entry on oeis.org

1, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 7, 5, 2, 3, 2, 3, 2, 2, 3, 7, 7, 2, 3, 5, 2, 3, 2, 3, 2, 2, 2, 11, 5, 2, 2, 5, 2, 2, 3, 7, 3, 2, 2, 5, 2, 2, 3, 7, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 13, 3, 2, 2, 5, 2, 3, 2, 2
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

Comments

Apart from the first term, it contains solely primes. Is every prime in there?
Apart from the first term and the definition, it is identical to the sequence A053760 by S. R. Finch.

Links

Crossrefs

Cf. A091380, A091381, A091383, A091384, A091385, A088192, A088198.

Programs

  • PARI
    {/* Distance of primes from the sequence of the largest "mixed" QR modulo the primes */ p_lqxr(to)=local(v=[1],k,r,q,p); for(i=2,to,p=prime(i);k=p-1;r=p%4-2; while(kronecker(k,p)<>r,k-=1); v=concat(v,p-k)); print(v) }

A091383 Prime numbers where the sequence of largest quadratic "mixed" residues modulo the primes (A091380) is non-monotonic.

Original entry on oeis.org

3, 7, 31, 71, 103, 151, 199, 239, 271, 311, 359, 463, 599, 719, 823, 839, 911, 1063, 1231, 1279, 1303, 1439, 1559, 1871, 1879, 1951, 1999, 2143, 2239, 2311, 2351, 2383, 2399, 2551, 2711, 2791, 3191, 3391, 3463, 3559, 3583, 3823, 3911, 3919, 4079, 4159
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

Comments

All of these primes belong to the +-1 least absolute reside classes modulo 8. (Tested for 10^5 primes.)
Where does this first differ from A088193 (if at all)? - R. J. Mathar, Aug 27 2025

Links

Crossrefs

Cf. A091380, A091381, A091382, A091384, A091385, A088190, A088193, A088199.

Programs

  • PARI
    {/* The primes where the sequence of the largest "mixed" QR modulo the primes is non-monotonic */ lqxr_nm_p(to)=local(v=[],k,r,q,p,e=1,n=0,i=1); while(nr,k-=1); if(k-e<=0,v=concat(v,p);n+=1);e=k); print(i);print(v) }

A091384 Members of the difference sequence (A091381) of the sequence of largest quadratic "mixed" residues modulo the primes (A091380) where the latter is non-monotonic.

Original entry on oeis.org

0, -1, -5, -1, -3, 0, 0, -8, 0, -1, 0, -7, -2, -6, -1, 0, 0, -5, -6, 0, 0, -7, -2, 0, -2, -3, -1, 0, -1, -5, -5, -7, -2, -11, 0, -1, 0, 0, -1, -2, -10, 0, 0, -6, -3, -1, -5, -5, -6, -5, 0, -1, -5, -7, -2, -5, -1, -5, 0, -2, -2, -7, 0, -7, -9, -4, -4, -8, -5, -13, 0, -4, -4, -7, -17, 0, -3, 0, -5, -1, -3, 0, -17, 0, -7, -6, -1, -2, -3, -3, 0
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

Comments

The negative values are either primes or composites (Cf. A088200).

Links

Crossrefs

Cf. A091380, A091381, A091382, A091383, A091385, A088190, A088196, A088200.

Programs

  • PARI
    {/* The difference sequence values where the sequence of the largest "mixed" QR modulo the primes is non-monotonic */ lqxr_nm_d(to)=local(v=[],k,r,q,p,e=1,n=0,i=1); while(nr,k-=1); if(k-e<=0,v=concat(v,k-e);n+=1);e=k); print(i);print(v) }

A091385 Distance (A091382) of primes from the largest quadratic "mixed" residues modulo the primes (A091380), where the latter is non-monotonic.

Original entry on oeis.org

2, 7, 11, 7, 11, 11, 7, 17, 7, 7, 7, 13, 11, 13, 7, 11, 7, 11, 13, 7, 11, 13, 11, 7, 11, 11, 13, 7, 7, 11, 13, 19, 11, 17, 11, 7, 7, 7, 13, 13, 17, 11, 11, 17, 11, 13, 19, 11, 13, 11, 7, 7, 11, 19, 11, 11, 7, 13, 11, 11, 13, 13, 7, 13, 17, 13, 11, 17, 11, 19, 11, 11, 11, 13, 23, 7, 17, 7
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

Comments

For n > 1, the values are some odd primes, but never < 7. The maximum value increases very slowly, it only reaches 43 for the first 10^5 primes.

Links

Crossrefs

Cf. A091380, A091381, A091382, A091383, A091384, A088195, A088201.

Programs

  • PARI
    {/* The distance of LQxR from the primes where the sequence of the largest "mixed" QR modulo the primes is non-monotonic */ lqxr_nm_pd(to)=local(v=[],k,r,q,p,e=1,n=0,i=1); while(nr,k-=1); if(k-e<=0,v=concat(v,p-k);n+=1);e=k); print(i);print(v) }
Showing 1-5 of 5 results.

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