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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A135275 a(n) = prime(2n-1) + prime(2n) - prime(2n+1).

Original entry on oeis.org

0, 1, 7, 13, 21, 27, 37, 41, 53, 65, 69, 75, 95, 101, 95, 121, 127, 143, 153, 161, 169, 187, 185, 207, 223, 231, 235, 251, 263, 275, 269, 305, 299, 321, 343, 345, 361, 373, 385, 391, 409, 425, 433, 445, 457, 459, 479, 493, 507, 517
Offset: 1

Views

Author

Cino Hilliard, Dec 02 2007

Keywords

Comments

Original name was: Sum and difference of staircase primes according to the rule: bottom + top - next top.

Links

Crossrefs

Cf. A096379, A135274.

Programs

  • Mathematica
    Table[Prime[n + 1] + Prime[n] - Prime[n + 2], {n, 1, 30}][[;; ;; 2]] (* G. C. Greubel, Oct 08 2016 *)
  • PARI
    g(n) = forstep(x=1,n,2,y=prime(x+1)+ prime(x)- prime(x+2);print1(y","))
  • PARI
    n=1; p=2; q=3; forprime(r=5,1e3, if(n, print1(p+q-r", ")); n=!n; p=q; q=r) \\ Charles R Greathouse IV, Oct 08 2016

Formula

We list the primes in staircase fashion as in A135274. The right diagonal, RD(n), is the set of top primes and the left diagonal, LD(x), is the set of bottom primes. Then a(n) = LD(n+1) + RD(n) - RD(n+2).
a(n) = A096379(2*n-1). - R. J. Mathar, Sep 10 2016

Extensions

New name from Charles R Greathouse IV, Oct 08 2016

A135277 a(n) = prime(2n-1) + prime(2n) + prime(2n+1).

Original entry on oeis.org

10, 23, 41, 59, 83, 109, 131, 159, 187, 211, 235, 269, 301, 319, 349, 395, 425, 457, 487, 519, 551, 581, 607, 661, 689, 713, 749, 789, 817, 841, 883, 931, 961, 1015, 1049, 1079, 1119, 1151, 1187, 1229, 1271, 1303, 1331, 1367, 1391, 1433, 1477, 1511, 1553, 1611
Offset: 1

Views

Author

Cino Hilliard, Dec 02 2007

Keywords

Comments

Original name was: Sum of staircase primes according to the rule: bottom + top + next top.

Links

Crossrefs

Cf. A034961, A135274.

Programs

  • Mathematica
    Table[Prime[n + 1] + Prime[n] + Prime[n + 2], {n, 1, 50}][[;; ;; 2]] (* G. C. Greubel, Oct 08 2016 *)
  • PARI
    g(n) = forstep(x=1,n,2,y=prime(x+1) + prime(x) + prime(x+2);print1(y","))
  • PARI
    a(n) = prime(2*n-1) + prime(2*n) + prime(2*n+1) \\ Charles R Greathouse IV, Oct 08 2016
  • Python
    from sympy import prime
def a(n): return prime(2*n-1) + prime(2*n) + prime(2*n+1)
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Oct 23 2021

Formula

We list the primes in staircase fashion as in A135274. The right diagonal, RD(n), is the set of top primes and the left diagonal, LD(n), is the set of bottom primes. Then a(n) = LD(n+1) + RD(n) + RD(n+2).
a(n) = A034961(2*n-1). - R. J. Mathar, Sep 10 2016

Extensions

New name from Charles R Greathouse IV, Oct 08 2016
Showing 1-2 of 2 results.

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