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.

A084106 Larger difference (r-q or q-p) associated with A084105.

Original entry on oeis.org

2, 6, 14, 10, 12, 18, 22, 24, 28, 30, 34, 42, 52, 54, 58, 60, 70, 82, 90, 100, 118, 132, 136, 148, 150, 168, 178, 196, 208, 214, 220, 234, 250, 288, 310, 318, 330, 360, 366, 384, 390, 402, 408, 414, 454, 462, 516, 588, 598, 610, 648, 706, 712, 736, 754, 756, 760
Offset: 1

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Author

Hugo Pfoertner, May 29 2003

Keywords

Comments

Differences > a(46) = 462 require search beyond 10^12. - Hugo Pfoertner, Sep 02 2020
Searched range through 10^13. - Hugo Pfoertner, Sep 17 2020

Examples

			a(5)=12 because the larger difference between A084105(5)=199 and its prime neighbors 197 and 211 is 211-199=12.
a(51)=648 corresponds to the gaps between the 3 consecutive primes 9787731507761, 9787731508409, 9787731508411. - _Hugo Pfoertner_, Sep 19 2020

Crossrefs

Cf. A002386, A084105, A337489.

Programs

  • PARI
    default(realprecision,20); default(primelimit,436270000); { apt(m)= local(dl,dr,q,qm); qm=1.0; for(n=2,m, dl=prime(n)-prime(n-1); dr=prime(n+1)-prime(n); q=min(dl,dr)/max(dl,dr)+0.; if(q
  • PARI
    a084106(limit)={my(p1=2,p2=3,q=0);forprime(k=5,limit,my(r=max((p2-p1)/(k-p2),(k-p2)/(p2-p1)));if(r>q,q=r;print1(max(p2-p1,k-p2),", "));p1=p2;p2=k)};
a084106(10^9) \\ Hugo Pfoertner, Sep 02 2020

Extensions

More terms from Don Reble and Jason Earls, May 29 2003
a(36)-a(46) from Hugo Pfoertner, Sep 02 2020
a(47)-a(51) from Hugo Pfoertner, Sep 17 2020
a(52)-a(57) from Martin Ehrenstein, Aug 07 2021

A329158 Let P1>=3, P2, P3 be consecutive primes, with P3-P2=2. a(n)=(P2+P3)/12 when P2-P1 sets a record.

Original entry on oeis.org

1, 2, 5, 25, 87, 192, 500, 1158, 1668, 4217, 4713, 5955, 17127, 28905, 61838, 76967, 96147, 139725, 260342, 1061923, 1205080, 4663498, 8871842, 11732765, 32534740, 42313103, 77638122, 92523718, 282054523, 728833340, 2940948542, 3344803093, 11810906035
Offset: 1

Views

Author

Hugo Pfoertner, Nov 06 2019

Keywords

Comments

6*a(n)-1, 6*a(n)+1 are twin primes such that the prime gap immediately preceding 6*a(n)-1 sets a record. The corresponding gap lengths are provided in A329159.

Crossrefs

Cf. A002822, A084105, A329159, A329160, A329161, A329164, A329165.

Programs

  • PARI
    p1=3;p2=5;r=0;forprime(p3=7,1e9,if(p3-p2==2,d=p2-p1;if(d>r,r=d;print1((p2+p3)/12,", ")));p1=p2;p2=p3)

A329160 Let P1>=5, P2, P3 be consecutive primes, with P2-P1=2. a(n)=(P1+P2)/12 when P3-P2 sets a record.

Original entry on oeis.org

1, 5, 23, 33, 87, 278, 495, 1293, 2027, 2690, 4245, 6773, 13283, 24938, 28893, 44270, 67475, 139708, 224922, 315893, 971000, 1723960, 3319792, 6228255, 7013717, 13194622, 25321985, 31864375, 32163975, 65155398, 86090027, 381175405, 452803425
Offset: 1

Views

Author

Hugo Pfoertner, Nov 08 2019

Keywords

Comments

6*a(n)-1, 6*a(n)+1 are twin primes such that the prime gap immediately following 6*a(n)+1 sets a record. The corresponding gap lengths are provided in A329161.

Examples

			See A329161.

Crossrefs

Cf. A002822, A084105, A329158, A329159, A329161, A329164, A329165.

Programs

  • PARI
    p1=5; p2=7; r=0; forprime(p3=11, 1e9, if(p2-p1==2, d=p3-p2; if(d>r, r=d; print1((p1+p2)/12, ", "))); p1=p2; p2=p3)
Showing 1-3 of 3 results.

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

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