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 1-10 of 10 results.

A045924 Numbers n such that prime(n) == -1 (mod n).

Original entry on oeis.org

1, 2, 3, 4, 10, 70, 72, 182, 440, 1053, 6458, 6461, 6471, 40087, 40089, 251737, 251742, 637320, 637334, 637336, 1617173, 4124466, 10553445, 10553455, 10553569, 10553570, 10553574, 10553576, 10553819, 10553829, 27067100, 27067262, 69709705, 69709719, 69709734, 69709873
Offset: 1

Views

Author

Len Smiley

Keywords

Comments

Same as n such that n divides A008864(n). - David James Sycamore, Jul 23 2018
Also numbers n such that prime(n) == n-1 (mod n). - Muniru A Asiru, Jul 24 2018

Examples

			10 is a member because the 10th prime, 29, is congruent to -1 mod 10.

Links

Crossrefs

Cf. A004648 and esp. A023143.
Cf. A052013, A048891, A092044, A092045, A092046, A092047, A092048, A092049, A092050, A092051, A092052, A008864.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[Mod[p = NextPrim[p], n] == n - 1, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
  • PARI
    isok(n) = Mod(prime(n), n) == -1; \\ Michel Marcus, Jul 24 2018

Extensions

More terms from Patrick De Geest, Nov 15 1999
Terms a(33) and beyond from Giovanni Resta, Feb 23 2020

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

A023146 Numbers k such that prime(k) == 4 (mod k).

Original entry on oeis.org

1, 75, 77, 637331, 637333, 637341, 637343, 27067053, 179992917, 8179002205, 2636913002917, 6201265271239157, 6201265271239347, 6201265271239413, 6201265271239981, 6201265271240331, 6201265271240341, 2159986889494445405, 2159986889494445525, 2159986889494445615
Offset: 1

Views

Author

David W. Wilson

Keywords

Examples

			The 75th prime is 379 and 379 == 4 (mod 75). Hence 75 is in the sequence.
The 76th prime is 383, but 383 == 3, not 4, (mod 76). So 76 is not in the sequence.

Crossrefs

Cf. A171431, A092046.
Cf. A023143, A023144, A023145, A023147, A023148, A023149, A023150, A023151, A023152.

Programs

  • Mathematica
    nextPrime[n_] := Block[{k = n + 1}, While[!PrimeQ[k], k++]; k]; p = 1; Do[If[Mod[p = nextPrime[p], n] == 4, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
Select[Range[1000], Mod[Prime[#], #] == 4 &] (* Alonso del Arte, Nov 16 2018 *)
  • Sage
    def A023146(max) :
    terms = []
    p = 2
    for n in range(1, max+1) :
        if (p - 4) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

More terms from Robert G. Wilson v, Feb 18 2004
2 more terms from Giovanni Resta and Robert G. Wilson v, Feb 22 2006
First term inserted by Eric M. Schmidt, Feb 05 2013
a(11)-a(20) from Giovanni Resta, Feb 23 2020

A092045 Numbers n such that prime(n) == -3 (mod n).

Original entry on oeis.org

1, 2, 25, 26, 68, 1054, 1058, 6472, 251723, 4124468, 69709727, 69709942, 465769817, 465769835, 1208198860, 8179002154, 8179002176, 8179002178, 145935689360, 145935689369, 145935689392, 145935689393
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Crossrefs

Cf. A023145, A045924, A092044, A092046, A092047, A092048, A092049, A092050, A092051, A092052.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == n - 3, Print[n]], {n, 1, 10^9}]
Join[{1,2},Select[Range[5 10^6],Mod[Prime[#],#]==#-3&]] (* Harvey P. Dale, Mar 29 2023 *)

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004
a(13)-a(22) from Robert G. Wilson v, Feb 22 2006

A092051 Numbers n such that prime(n) == -9 (mod n).

Original entry on oeis.org

1, 2, 4, 5, 17, 19, 20, 22, 23, 64, 1055, 1057, 6463, 251708, 251743, 251744, 251755, 251758, 27067054, 27067118, 27067138, 69709681, 69709703, 69709712, 145935689366, 382465573490, 382465573498, 6935812012621, 126979448983610, 885992692751476
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Links

Crossrefs

Cf. A023151, A045924, A092044, A092045, A092046, A092047, A092048, A092049, A092050, A092052.

Programs

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

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004
a(25) from Robert G. Wilson v, Feb 22 2006
Terms a(26) and beyond from Giovanni Resta, Feb 23 2020

A092047 Numbers n such that prime(n) == -5 (mod n).

Original entry on oeis.org

1, 2, 4, 6, 8, 27, 28, 169, 183, 187, 188, 189, 438, 442, 1056, 1059, 40084, 40088, 40091, 40114, 40121, 100348, 251709, 4124588, 10553499, 10553853, 27066972, 179992914, 179992932, 179993012, 465769812, 1208198618, 1208198852
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Crossrefs

Cf. A023147, A045924, A092044, A092045, A092046, A092048, A092049, A092050, A092051, A092052.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == n - 5, Print[n]], {n, 1, 10^9}]

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004
a(28)-a(34) from Robert G. Wilson v, Feb 22 2006

A092048 Numbers n such that prime(n) == -6 (mod n).

Original entry on oeis.org

1, 439, 100349, 100361, 100363, 27066991, 27067117, 1208198633, 8179002133
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Crossrefs

Cf. A023148, A045924, A092044, A092045, A092046, A092047, A092049, A092050, A092051, A092052.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == n - 6, Print[n]], {n, 1, 10^9}]

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004
a(8)-a(9) from Robert G. Wilson v, Feb 22 2006

A092049 Numbers n such that prime(n) == -7 (mod n).

Original entry on oeis.org

1, 2, 3, 24, 29, 30, 170, 171, 173, 176, 178, 184, 185, 186, 2616, 6462, 6467, 6470, 40090, 40115, 40118, 40120, 637330, 10553400, 10553441, 10553451, 10553458, 10553503, 10553548, 27067046, 27067134, 27067136, 69709702, 69709704, 69709716
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Crossrefs

Cf. A023149, A045924, A092044, A092045, A092046, A092047, A092048, A092050, A092051, A092052.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == n - 7, Print[n]], {n, 1, 10^9}]

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004

A092050 Numbers n such that prime(n) == -8 (mod n).

Original entry on oeis.org

1, 63, 435, 100347, 100353, 100359, 637335, 129992911, 129993001, 129993007, 129993171, 8179002121, 8179002123, 8179002177, 382465573539
Offset: 1

Views

Author

Robert G. Wilson v, Feb 18 2004

Keywords

Comments

No more terms < 2*10^12. - David Wasserman, Jun 09 2005

Crossrefs

Cf. A023150, A045924, A092044, A092045, A092046, A092047, A092048, A092049, A092051, A092052.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == n - 8, Print[n]], {n, 1, 10^9}]

Extensions

Corrected by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 20 2004
More terms from David Wasserman, Jun 09 2005

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
Showing 1-10 of 10 results.

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