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 1-8 of 8 results.

A023144 Numbers k such that prime(k) == 2 (mod k).

Original entry on oeis.org

1, 3, 13, 15, 69, 73, 637321, 27066989, 27067095, 27067133, 179992909, 1208198629, 1208198853, 8179002209, 382465573515, 2636913003191, 18262325820323, 18262325820339, 6201265271239163, 6201265271239191, 6201265271239431, 43525513764815041, 43525513764815125
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

a(15) > 10^13. - Charles R Greathouse IV, Mar 17 2011

Links

Crossrefs

Cf. A092044, A023143, A023145, A023146, A023147, A023148, A023149, A023150, A023151, A023152.
Cf. A105290.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 2, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)

Extensions

More terms from Robert G. Wilson v, Feb 18 2004
a(10)-a(13) from Giovanni Resta and Robert G. Wilson v, Feb 22 2006
Missing first term inserted by M. F. Hasler, Feb 04 2009
a(15)-a(23) from Giovanni Resta, Oct 02 2019

A092044 Numbers n such that prime(n) == -2 (mod n).

Original entry on oeis.org

1, 11, 71, 637319, 637323, 637327, 179993015, 1208198861, 8179002163, 8179002189, 55762149067, 55762149103, 6201265271239787, 43525513764814971, 43525513764815121, 2159986889494444325, 2159986889494445481, 2159986889494445499, 2159986889494447181
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Crossrefs

Cf. A023144, A045924, A092045, A092046, A092047, A092048, A092049, A092050, A092051, A092052.
Cf. A105290.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == n - 2, Print[n]], {n, 1, 10^9}]
  • PARI
    for(i=1,10^9,if(Mod(prime(i),i)==-2,print1(i,",")));

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004
a(7)-a(12) from Robert G. Wilson v, Feb 22 2006
a(13)-a(19) from Giovanni Resta, Feb 23 2020

A105286 Numbers k such that prime(k+1) == 1 (mod k).

Original entry on oeis.org

1, 2, 3, 10, 24, 25, 66, 168, 182, 186, 187, 188, 438, 6462, 40071, 40084, 40085, 40091, 40108, 40118, 251745, 637224, 637306, 637336, 637338, 10553441, 10553445, 10553452, 10553479, 10553515, 10553550, 10553829, 27067032, 27067054, 27067134, 69709710, 69709713, 179992838, 179993008, 3140421868, 8179002150, 55762149074, 1003652347080, 1003652347109, 1003652347112, 1003652347352, 1003652347375
Offset: 1

Views

Author

Zak Seidov, Apr 25 2005

Keywords

Comments

If k is a term, then prime(k+1)^prime(k+1) is a reverse Meertens number in base prime(k+1)^((prime(k+1)-1)/k). - Chai Wah Wu, Dec 14 2022
Integers k such that A004649(k+1) = 1. - Michel Marcus, Dec 30 2022

Links

Crossrefs

Cf. A004649, A105287, A105288, A105290, A105329, A105451.

Programs

  • Mathematica
    bb={};Do[If[1==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb
  • Python
    from itertools import count, islice
from sympy import prime
def A105286_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda k: not (prime(k+1)-1)%k,count(max(startvalue,1)))
A105286_list = list(islice(A105286_gen(),10)) # Chai Wah Wu, Dec 14 2022
  • Sage
    def A105286(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 1) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

More terms from Farideh Firoozbakht, May 12 2005
First term inserted by Eric M. Schmidt, Feb 05 2013
More terms from Michel Marcus, Dec 29 2022
a(40)-a(47) from Max Alekseyev, Aug 31 2024

A105329 Numbers k such that prime(k+1) == 5 (mod k).

Original entry on oeis.org

1, 2, 6, 7, 12, 14, 181, 1053, 1057, 2614, 40089, 40114, 40117, 40119, 100346, 100352, 100358, 251707, 251742, 251743, 251754, 251757, 1617173, 4124458, 10553513, 27067262, 27067272, 179992922, 179992932, 179993012, 179993172, 3140421806, 3140421838, 3140421866, 3140421872, 55762149076, 145935689366
Offset: 1

Views

Author

Zak Seidov, Apr 30 2005

Keywords

Comments

There are no further terms up to 215000000. - Farideh Firoozbakht, May 13 2005
Integers k such that A004649(k+1) = 5. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105287, A105288, A105290, A105451.

Programs

  • Mathematica
    Do[If[5 == Mod[Prime[n + 1], n], bb = Append[bb, n]], {n, 1, 251758}];
bb={};Do[If[5 == Mod[Prime[n + 1], n], bb = Append[bb, n]], {n, 1, 251758}];bb  (* Farideh Firoozbakht, May 13 2005 *)
  • Sage
    def A105329(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 5) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

More terms from Farideh Firoozbakht, May 13 2005
First two terms inserted by Eric M. Schmidt, Feb 05 2013
a(28)-a(29) corrected, a(30)-a(37) added by Max Alekseyev, Aug 31 2024

A105287 Numbers k such that prime(k+1) == 2 (mod k).

Original entry on oeis.org

1, 9, 67, 437, 441, 2615, 100349, 100353, 100359, 637197, 637305, 27066969, 27067049, 27067101, 27067113, 27067115, 179992839, 179993001, 55762149071, 382465573491
Offset: 1

Views

Author

Zak Seidov, Apr 25 2005

Keywords

Comments

Integers k such that A004649(k+1) = 2. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105288, A105290, A105329, A105451.

Programs

Extensions

First term inserted by Eric M. Schmidt, Feb 05 2013
More terms from Harvey P. Dale, May 04 2013
a(12)-a(18) from Michel Marcus, Dec 29 2022
a(19)-a(20) from Max Alekseyev, Aug 31 2024

A105288 Numbers k such that prime(k+1) == 3 (mod k).

Original entry on oeis.org

1, 2, 4, 5, 70, 440, 1055, 1058, 6461, 6466, 6469, 251752, 4124468, 27067036, 27067112, 69709709, 69709957, 465769835, 8179002104, 145935689357, 382465573490
Offset: 1

Views

Author

Zak Seidov, Apr 25 2005

Keywords

Comments

Integers k such that A004649(k+1) = 3. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105287, A105290, A105329, A105451.

Programs

  • Magma
    [1,2] cat [n: n in [1..2*10^4] | NthPrime(n+1) mod n eq 3]; // Vincenzo Librandi, May 02 2018
  • Maple
    n:= 0: p:= 2: count:= 0:
for n from 1 while count < 13 do
p:= nextprime(p);
if p-3 mod n = 0 then
    count:= count+1;
  A[count]:= n;
  fi
od:
seq(A[i],i=1..count); # Robert Israel, May 02 2018
  • Mathematica
    bb={};Do[If[3==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb
Join[{1, 2}, Select[Range[2 10^7], Mod[Prime[# + 1], #]==3 &]] (* Vincenzo Librandi, May 02 2018 *)
  • Sage
    def A105288(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 3) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

First two terms inserted by Eric M. Schmidt, Feb 05 2013
a(12)-a(13) from Robert Israel, May 02 2018
a(14)-a(21) from Giovanni Resta, May 02 2018

A105451 Numbers k such that prime(k+1) == 8 (mod k).

Original entry on oeis.org

1, 5, 15, 73, 75, 100347, 637329, 27067271, 179993015, 1208198523, 55762149023, 55762149103, 382465573515
Offset: 1

Views

Author

Zak Seidov, May 02 2005

Keywords

Comments

No additional terms up to 7 million. - Harvey P. Dale, Jan 23 2012
Integers k such that A004649(k+1) = 8. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105287, A105288, A105290, A105329.
Cf. A023150 (Numbers k such that prime(n) == 8 (mod k)).

Programs

  • Mathematica
    bb={};Do[If[8==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 1000000}];bb
Select[Range[700000],Mod[Prime[#+1],#]==8&] (* Harvey P. Dale, Jan 23 2012 *)
  • Python
    from sympy import nextprime
def A105451(max):
    terms = []
    p = 3
    for n in range(1, max+1):
        if (p - 8) % n == 0: terms.append(n)
        p = nextprime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

First two terms inserted by Eric M. Schmidt, Feb 05 2013
a(8)-a(10) from Michel Marcus, Dec 29 2022
a(11)-a(13) from Max Alekseyev, Aug 31 2024

A105421 Numbers k such that prime(k + 1) == 7 (mod k).

Original entry on oeis.org

1, 2, 3, 4, 8, 30, 31, 33, 68, 72, 180, 1052, 6471, 40083, 40087, 40090, 40113, 40120, 100348, 100360, 100362, 637334, 4124588, 10553439, 10553442, 10553455, 10553478, 10553505, 10553512, 10553827, 10553849, 69709712, 69709719, 69709728, 69709958, 21338685404, 1003652347332, 1003652347349, 1003652347360, 1003652347365
Offset: 1

Views

Author

Zak Seidov, May 02 2005

Keywords

Links

Crossrefs

Cf. A105286, A105287, A105288, A105290, A105329, A105451.

Programs

  • Mathematica
    Select[Range[650000],Mod[Prime[#+1]-7,#]==0&] (* Harvey P. Dale, Sep 23 2021 *)
  • PARI
    isok(n) = Mod(prime(n + 1), n) == Mod(7, n); \\ Michel Marcus, Apr 05 2015
  • PARI
    n=0;forprime(p=3,,if(Mod(p,n++)==7,print1(n", "))) \\ Charles R Greathouse IV, Jul 23 2015
  • Python
    def A105421(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 7) % n == 0 : terms.append(n)
        p = nextprime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

a(1)-a(4) inserted by Eric M. Schmidt, Feb 05 2013
a(19)-a(22) from Harvey P. Dale, Apr 05 2015
a(23)-a(35) from Manfred Scheucher, Jul 23 2015
a(36) from Charles R Greathouse IV, Jul 23 2015
a(37)-a(40) from Max Alekseyev, Aug 31 2024
Showing 1-8 of 8 results.

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