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.

User: Jean C. Lambry

Jean C. Lambry's wiki page.

Jean C. Lambry has authored 1 sequences.

A262182 Prime numbers of the form (n*(n+1)/2)^2 + 1.

Original entry on oeis.org

2, 37, 101, 1297, 4357, 14401, 44101, 90001, 164837, 246017, 608401, 894917, 1382977, 4326401, 8122501, 8561477, 9985601, 10497601, 38638657, 46049797, 52707601, 84272401, 121572677, 146168101, 165894401, 201526417, 259532101, 289680401, 404010001, 428738437
Offset: 1

Author

Jean C. Lambry, Oct 02 2015

Keywords

Comments

Sum_{n>=1} 1/a(n) = 0.538046187...

Crossrefs

Programs

  • Mathematica
    Select[Accumulate[Range[250]]^2+1,PrimeQ] (* Harvey P. Dale, Nov 14 2024 *)
  • PARI
    for(n=1, 1e3, if(isprime(k = (n*(n+1)/2)^2+1), print1(k", "))) \\ Altug Alkan, Oct 02 2015
  • Python
    def prime(n):
        if n == 1: return True
        d = n + 1
        c = n - 1
        while c > 0 and d % c:
            d += n
            c -= 1
        return bool(c == 1)
    n = 1
    i = 1
    while i <= 500:
        target = (i * (i + 1)) // 2
        if prime(target):
            print(n, target*target+1)
            n += 1
        i += 1
    # Jean C. Lambry, Oct 06 2015
    

Formula

a(n) = A154323(A217755(n)). - Michel Marcus, Oct 02 2015
a(n) = ((A217755(n)^2 + A217755(n))/2)^2 + 1. - Jean C. Lambry, Oct 07 2015

Extensions

More terms from Altug Alkan, Oct 02 2015