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.

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A069639 Smallest composite k such that phi(k) > k*(1-1/n^2).

Original entry on oeis.org

4, 25, 121, 289, 841, 1369, 2809, 4489, 6889, 10201, 16129, 22201, 29929, 38809, 51529, 66049, 85849, 109561, 134689, 160801, 196249, 237169, 292681, 332929, 398161, 458329, 537289, 619369, 727609, 822649, 935089, 1062961, 1190281
Offset: 1

Views

Author

Benoit Cloitre, Apr 21 2002

Keywords

Crossrefs

Cf. A000010 (phi), A007491, A007918, A069549.

Programs

  • Mathematica
    a[n_] := NextPrime[n^2]^2; Array[a, 40] (* Amiram Eldar, May 08 2025 *)
  • PARI
    a(n) = nextprime(n^2)^2; \\ Amiram Eldar, May 08 2025

Formula

a(n) = nextprime(n^2)^2 = A007918(n^2)^2.
a(n) = A007491(n)^2. - Amiram Eldar, May 08 2025

A187409 n^2 + nextprime(n^2).

Original entry on oeis.org

3, 9, 20, 33, 54, 73, 102, 131, 164, 201, 248, 293, 342, 393, 452, 513, 582, 655, 728, 801, 884, 971, 1070, 1153, 1256, 1353, 1462, 1571, 1694, 1807, 1928, 2055, 2180, 2319, 2454, 2593, 2742, 2891, 3044, 3201, 3374, 3541, 3710, 3885, 4052, 4245, 4422, 4613
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 09 2011

Keywords

Examples

			1^2+2=3, 2^2+5=9, 3^2+11=20,..

Crossrefs

Cf. A053000, A056927, A007491.

Programs

  • Mathematica
    Table[n2=n^2; NextPrime[n2]+n2, {n,100}]
#+NextPrime[#]&/@(Range[100]^2) (* Harvey P. Dale, Sep 20 2022 *)

A276556 a(n) = smallest prime p such that (smallest prime > p^2) == p^2 + 4n^2, n>=1.

Original entry on oeis.org

5, 281, 461, 4937, 25367, 75997, 1193909, 3464389, 48591863, 23674667, 22486333, 1648510979, 12708853771, 25139472583, 53498475287
Offset: 1

Views

Author

Zak Seidov, Apr 18 2017

Keywords

Examples

			5^2+4*1^2=29, 281^2+4*2^2=78977, 461^2 + 4*3^2=212557 (all prime).

Crossrefs

Cf. A007491, A053000.

Programs

  • Mathematica
    Table[p = 2; While[NextPrime[p^2] != p^2 + 4 n^2, p = NextPrime@ p]; p, {n, 8}] (* Michael De Vlieger, Apr 22 2017 *)
  • PARI
    a(n) = {forprime(p=2, , if (nextprime(p^2+1) == p^2 + 4*n^2, return (p)););} \\ Michel Marcus, Apr 19 2017

Extensions

a(13)-a(15) from Rémy Sigrist, Apr 28 2017
Previous Showing 31-33 of 33 results.

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

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