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.

Previous Showing 11-17 of 17 results.

A092052 Numbers n such that prime(n) == -10 (mod n).

Original entry on oeis.org

1, 3, 437, 2639, 4124589, 27067013, 27067101, 27067139, 27067271, 382465573551, 18262325820327, 18262325820329, 18262325820333, 885992692751831, 6201265271239783, 6201265271239997, 6201265271240071, 6201265271240403, 306268030480171331
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Crossrefs

Cf. A023152, A045924, A092044, A092045, A092046, A092047, A092048, A092049, A092050, A092051.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == n - 10, Print[n]], {n, 1, 10^9}]

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004
a(10)-a(19) from Giovanni Resta, Feb 23 2020

A116677 Numbers k such that prime(k) == 12 (mod k).

Original entry on oeis.org

1, 91, 4124467, 27067043, 27067229, 27067261, 27067523, 1208198857, 8179002137, 8179002191
Offset: 1

Views

Author

Giovanni Resta and Robert G. Wilson v, Feb 22 2006

Keywords

Crossrefs

Cf. A004648, A023143 - A023152, A116657, A116658, A116659: prime(n) == m (mod n), m=1..14.
Cf. A116678.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 12, Print[n]], {n, 10^9}]
  • Sage
    def A116677(max) :
    terms = []
    p = 2
    for n in range(1, max+1) :
        if (p - 12) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

First term inserted by Eric M. Schmidt, Feb 05 2013

A116657 Numbers k such that prime(k) == 11 (mod k).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 20, 38, 39, 82, 190, 192, 444, 2702, 40079, 40156, 251719, 251725, 251733, 251740, 251788, 637322, 637342, 10553424, 10553571, 10553575, 10553646, 10553824, 27066990, 69709708, 69709870, 69709881, 69709941, 179992918, 179993010
Offset: 1

Views

Author

Zak Seidov, Feb 21 2006

Keywords

Comments

Starting with a(7), positions of 11 in A004648. - corrected by Eric M. Schmidt, Feb 05 2013

Crossrefs

Cf. A004648; A023143 - A023152, A116657, A116677, A116658, A116659: prime(n) == m (mod n), m=1..14.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 11, Print[n]], {n, 10^9}] (* Robert G. Wilson v, Feb 22 2006 *)
  • Sage
    def A116657(max) :
    terms = []
    p = 2
    for n in range(1, max+1) :
        if (p - 11) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

a(17)-a(35) from Robert G. Wilson v, Feb 22 2006
First six terms inserted by Eric M. Schmidt, Feb 05 2013

A116658 Numbers k such that prime(k) == 13 (mod k).

Original entry on oeis.org

1, 2, 6, 12, 22, 40, 42, 84, 86, 90, 193, 2712, 16056, 16058, 40077, 40123, 40124, 40125, 251720, 251766, 251769, 251787, 637332, 10553432, 10553435, 10553501, 10553568, 10553817, 10553826, 27067042, 27067132, 69709722, 179993160, 465769803
Offset: 1

Views

Author

Zak Seidov, Feb 21 2006

Keywords

Comments

Starting with a(5), positions of 13 in A004648. - corrected by Eric M. Schmidt, Feb 05 2013

Crossrefs

Cf. A004648; A023143 - A023152, A116657, A116677, A116658, A116659: prime(n) == m (mod n), m=1..14.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 13, Print[n]], {n, 10^9}] (* Robert G. Wilson v, Feb 22 2006 *)
  • Sage
    def A116658(max) :
    terms = []
    p = 2
    for n in range(1, max+1) :
        if (p - 13) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

a(24)-a(34) from Robert G. Wilson v, Feb 22 2006
First four terms inserted by Eric M. Schmidt, Feb 05 2013

A116659 Numbers k such that prime(k) == 14 (mod k).

Original entry on oeis.org

1, 3, 9, 23, 81, 85, 87, 16057, 4124457, 27067011, 27067127, 1208198605, 1208198851
Offset: 1

Views

Author

Zak Seidov, Feb 21 2006

Keywords

Comments

Starting with a(4), positions of 14 in A004648. - Robert G. Wilson v, Feb 22 2006, corrected by Eric M. Schmidt, Feb 05 2013

Crossrefs

Cf. A004648; A023143 - A023152, A116657, A116677, A116658, A116659: prime(n) == m (mod n), m=1..14.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 14, Print[n]], {n, 10^9}] (* Robert G. Wilson v *)
  • Sage
    def A116659(max) :
    terms = []
    p = 2
    for n in range(1, max+1) :
        if (p - 14) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

a(9)-a(13) from Robert G. Wilson v, Feb 22 2006
First three terms inserted by Eric M. Schmidt, Feb 05 2013

A116662 Numbers k such that prime(k) == 15 (mod k).

Original entry on oeis.org

1, 2, 4, 13, 14, 41, 46, 446, 1066, 16054, 251713, 251738, 251764, 251789, 27067052, 27067124, 465769808, 465769816, 1208198606, 1208198632, 145935689368
Offset: 1

Views

Author

Zak Seidov, Feb 21 2006

Keywords

Comments

Starting with a(6), positions of 15 in A004648. - corrected by Eric M. Schmidt, Feb 05 2013

Crossrefs

Cf. A004648; A023143-A023152, A116657, A116677, A116658, A116659, prime(n) == m (mod n), m=1-10,11,12,13,14.

Programs

  • Python
    from gmpy2 import next_prime
def A116662(max) :
    terms = []
    p = 2
    for n in range(1, max+1) :
        if (p - 15) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms # Eric M. Schmidt, Feb 05 2013

Extensions

More terms from Ryan Propper, Jul 21 2006
a(21) from Donovan Johnson, Dec 07 2008
Edited by and first five terms inserted by Eric M. Schmidt, Feb 05 2013

A099641 Number of solutions to x*frac[p(x)/x]<=Log[n] or A004648(n)<=Log[n].

Original entry on oeis.org

1, 5, 6, 12, 13, 14, 15, 31, 32, 34, 69, 73, 74, 75, 76, 77, 181, 445, 1052, 6455, 6456, 6457, 6459, 6460, 6466, 15928, 16055, 40073, 40078, 40080, 40081, 40082, 40083, 40122, 100362, 100364, 100365, 251707, 251711, 251712, 251717, 251719, 251721
Offset: 1

Views

Author

Labos Elemer, Nov 02 2004

Keywords

Comments

Solutions appear in clusters because of features of diagram visible at A004648. Later clusters are introduced by 6455, 15928, 40073, 100362, 251707, 637235, 4124455, respectively.
Number of solutions in consecutive clusters seem to be as follows: 1,2,4,3,6,1,1,1,6,2,7,3 etc..

Crossrefs

Cf. A004648.
Cf. A023143-A023152, A072610.

Programs

  • Mathematica
    ta={{0}};Do[s=w*fra[Prime[w]/w];If[ !Greater[s, Log[n]], Print[w]; ta=Append[ta, w]], {w, 1, 1000000}];ta=Delete[ta, 1]
Previous Showing 11-17 of 17 results.

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

Content is available under The OEIS End-User License Agreement.