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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A166119 a(n) = A165966(n)/12.

Original entry on oeis.org

3, 10, 23, 25, 213, 270, 455, 688, 1060, 1953, 2233, 2915, 3468, 3838, 4718, 4945, 8645, 10230, 11638, 12308, 13090, 15428, 16250, 19295, 23095, 27778, 29435, 32230, 33488, 43053, 50830, 71668, 83485, 86460, 89365, 96330, 104610, 106600, 127823
Offset: 1

Views

Author

Zak Seidov, Oct 07 2009

Keywords

Comments

The only known primes in the sequence are 3, 23.

Crossrefs

Cf. A000217, A001359, A086816, A105174, A111163, A165966.

Programs

  • PARI
    lista(nn) = {for (n = 1, nn, trg = n*(n+1)/2; if (!(trg % 2) && isprime(trg/2-1) && isprime(trg/2+1), print1(trg/12, ", ")););} \\ Michel Marcus, Oct 16 2013

Formula

a(n) = (A086816(n) + 1)/6. - Alois P. Heinz, Sep 18 2024

A105174 Numbers k such that k*(k+1)/4 - 1 and k*(k+1)/4 + 1 are twin primes.

Original entry on oeis.org

8, 15, 23, 24, 71, 80, 104, 128, 159, 216, 231, 264, 288, 303, 336, 344, 455, 495, 528, 543, 560, 608, 624, 680, 744, 816, 840, 879, 896, 1016, 1104, 1311, 1415, 1440, 1464, 1520, 1584, 1599, 1751, 1871, 1896, 1920, 1976, 2015, 2016, 2055, 2088, 2103, 2175
Offset: 1

Views

Author

Pierre CAMI, Apr 11 2005

Keywords

Comments

The twin primes are = (sum of numbers from 1 to k)/2 -1 and +1.

Examples

			8*9/4=18, 17 and 19 twin primes so a(1)=8
15*16/4=60, 59 and 61 twin primes so a(2)=15

Links

Crossrefs

Cf. A001097, A001359, A006512, A165966.

Programs

  • Mathematica
    Select[Range[2200],AllTrue[(#(#+1))/4+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 01 2015 *)

Extensions

More terms from Zak Seidov, Oct 07 2009
Showing 1-2 of 2 results.

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