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 1-7 of 7 results.

A054321 Smallest prime greater than 5^n.

Original entry on oeis.org

2, 7, 29, 127, 631, 3137, 15629, 78137, 390647, 1953151, 9765629, 48828139, 244140683, 1220703131, 6103515637, 30517578167, 152587890649, 762939453127, 3814697265637, 19073486328181, 95367431640673, 476837158203149
Offset: 0

Views

Author

Robert G. Wilson v, Aug 14 2001

Keywords

Links

Crossrefs

Cf. A014210, A014211, A013599 (a(n)-5^n).

Programs

  • Maple
    seq(nextprime(5^n),n=0..100); # Robert Israel, May 19 2014
  • Mathematica
    NextPrime[ n_Integer] := (k = n + 1; While[ !PrimeQ[k], k++ ]; k); Table[ NextPrime[5^n], {n, 0, 22} ] (* Mathematica 5 and below *)
NextPrime[5^Range[0,25]] (* Mathematica 6; Harvey P. Dale, Jun 19 2011 *)
  • PARI
    a(n)=nextprime(5^n+1) \\ Charles R Greathouse IV, Jun 19 2011

A127796 a(n) = nextprime(9^n) - 9^n.

Original entry on oeis.org

1, 2, 2, 4, 2, 2, 16, 2, 26, 10, 8, 4, 2, 2, 26, 4, 70, 34, 2, 8, 118, 4, 8, 68, 56, 28, 50, 28, 62, 158, 16, 122, 92, 28, 20, 110, 140, 70, 28, 44, 20, 124, 316, 38, 8, 44, 136, 58, 110, 2, 148, 170, 116, 170, 40, 2, 182, 10, 46, 254, 56, 14, 8, 2, 190, 148, 382, 10, 56, 10
Offset: 0

Views

Author

Artur Jasinski, Jan 29 2007

Keywords

Links

Crossrefs

Cf. A013597, A013598, A013602, A013599, A013600, A013601, A127796, A033873, A127797, A127798, A127799.
Cf. A013632, A001019.

Programs

  • Mathematica
    << NumberTheory`NumberTheoryFunctions` a = {}; Do[k = NextPrime[9^x] - 9^x; AppendTo[a, k], {x, 0, 100}]; a

Formula

a(n) = A013632(A001019(n)). - Michel Marcus, Nov 18 2019

A127797 Nextprime(11^n)-11^n.

Original entry on oeis.org

1, 2, 6, 30, 12, 2, 46, 20, 10, 2, 28, 62, 28, 42, 70, 30, 18, 20, 10, 18, 136, 102, 100, 30, 96, 6, 6, 68, 228, 30, 46, 48, 46, 32, 166, 36, 96, 42, 70, 278, 12, 108, 60, 42, 136, 68, 30, 18, 72, 36, 72, 30, 226, 252, 340, 126, 10, 42, 18, 182, 58, 18, 16, 120, 138, 36, 10
Offset: 0

Views

Author

Artur Jasinski, Jan 29 2007

Keywords

Crossrefs

Cf. A013597, A013598, A013602, A013599, A013600, A013601, A127796, A033873, A127795, A127796, A127798, A127799.

Programs

  • Mathematica
    << NumberTheory`NumberTheoryFunctions` a = {}; Do[k = NextPrime[11^x] - 11^x; AppendTo[a, k], {x, 0, 100}]; a

A127798 Nextprime(12^n)-12^n.

Original entry on oeis.org

1, 1, 5, 5, 7, 7, 7, 25, 5, 31, 49, 31, 35, 25, 23, 11, 17, 29, 47, 103, 7, 5, 7, 23, 133, 19, 5, 13, 7, 215, 89, 5, 53, 89, 17, 35, 257, 29, 19, 193, 13, 121, 79, 71, 53, 61, 287, 61, 107, 125, 5, 203, 23, 119, 89, 5, 95, 61, 7, 29, 191, 211, 119, 31, 377, 37, 49, 89, 161, 5, 785
Offset: 0

Views

Author

Artur Jasinski, Jan 29 2007

Keywords

Crossrefs

Cf. A013597, A013598, A013602, A013599, A013600, A013601, A127796, A033873, A127795, A127796, A127797, A127799.

Programs

  • Mathematica
    << NumberTheory`NumberTheoryFunctions` a = {}; Do[k = NextPrime[12^x] - 12^x; AppendTo[a, k], {x, 0, 100}]; a
f[n_]:=Module[{c=12^n},NextPrime[c]-c]; f/@Range[0,100]  (* Harvey P. Dale, Mar 19 2011 *)

A127799 Nextprime(13^n)-13^n.

Original entry on oeis.org

1, 4, 4, 6, 10, 6, 4, 6, 18, 46, 4, 34, 22, 16, 58, 4, 72, 28, 42, 34, 30, 166, 60, 16, 136, 46, 94, 66, 276, 30, 70, 136, 70, 18, 60, 142, 228, 10, 462, 12, 28, 166, 138, 12, 376, 16, 180, 102, 222, 228, 102, 126, 108, 46, 24, 172, 162, 6, 114, 6, 108, 6, 72, 84, 22, 70
Offset: 0

Views

Author

Artur Jasinski, Jan 29 2007

Keywords

Crossrefs

Cf. A013597, A013598, A013602, A013599, A013600, A013601, A127796, A033873, A127795, A127796, A127797, A127798.

Programs

  • Mathematica
    np13[n_]:=Module[{c=13^n},NextPrime[c]-c]; Array[np13,70,0] (* Harvey P. Dale, Mar 31 2012 *)

A127795 Nextprime(8^n)-8^n.

Original entry on oeis.org

1, 3, 3, 9, 3, 3, 3, 17, 43, 29, 3, 17, 31, 23, 15, 59, 21, 21, 159, 9, 33, 29, 9, 29, 15, 33, 7, 17, 3, 39, 133, 105, 61, 255, 267, 39, 33, 51, 43, 29, 451, 165, 7, 17, 67, 33, 87, 5, 175, 51, 147, 95, 45, 299, 19, 141, 87, 129, 7, 75, 15, 215, 205, 35, 133, 35, 15, 351, 7, 203
Offset: 0

Views

Author

Artur Jasinski, Jan 29 2007

Keywords

Comments

"Nextprime(k)" is not well-defined: it can mean the smallest prime >= k or the smallest prime > k. Of course here it does not matter. - N. J. A. Sloane, Jan 31 2007

Crossrefs

Cf. A013597, A013598, A013602, A013599, A013600, A013601, A127796, A033873, A127797, A127798, A127799.

Programs

  • Mathematica
    np[n_]:=Module[{n8=8^n},NextPrime[n8]-n8]; Array[np,70,0] (* Harvey P. Dale, Jun 20 2011 *)

Extensions

Erroneous Mathematica program deleted by Harvey P. Dale, Jun 20 2011

A338419 (Smallest prime >= 5^n) - (largest prime <= 5^n).

Original entry on oeis.org

0, 6, 14, 12, 16, 10, 16, 66, 42, 10, 26, 70, 58, 14, 46, 86, 18, 114, 72, 74, 78, 72, 74, 96, 78, 14, 50, 76, 78, 130, 110, 286, 164, 170, 424, 154, 70, 132, 336, 162, 160, 90, 400, 342, 144, 36, 208, 108, 284, 98, 138, 216, 20, 66, 132, 504, 320, 120, 354
Offset: 1

Views

Author

A.H.M. Smeets, Oct 25 2020

Keywords

Comments

Size of prime gap containing the number 5^n, for n > 1.
From Gauss's prime counting function approximation, the expected gap size should be approximately n*log(5), however, the observed values seem to be closer to n*log(25) = n*A016648.
The arithmetic mean of a(n)/n for the terms 2..500 is 3.220 ~ 2*log(5) = A016648.

Links

Crossrefs

Cf. A013599, A013605, A016648.
Cf. A058249 (2^n), A338155 (3^n), A338376 (6^n), A038804 (10^n).

Programs

  • Mathematica
    a[1] = 0; a[n_] := First @ Differences @ NextPrime[5^n, {-1, 1}]; Array[a, 60] (* Amiram Eldar, Oct 30 2020 *)
  • PARI
    a(n) = if (n==1, 0, my(pw=5^n); nextprime(pw+1) - precprime(pw-1)); \\ Michel Marcus, Oct 27 2020

Formula

a(n) = A013599(n) + A013605(n) for n > 1.
Showing 1-7 of 7 results.

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

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