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 1-4 of 4 results.

A110854 A155750(n)-A155067(n) = prime(2n+2)-prime(2n+1)-prime(2n)+prime(2n-1).

Original entry on oeis.org

1, 0, 0, 4, 0, -4, 4, -4, 2, 2, 0, -2, 0, 0, 0, -2, 0, 4, 0, -4, 0, 0, 10, -10, 4, 4, -4, -4, 2, 6, -6, 0, 2, -4, 4, 0, -2, 4, 0, -6, 0, 2, 4, -6, 10, -8, 0, 8, 6, -8, -4, 0, 0, -4, 4, -4, 8, -6, 2, 6, -6, 4, 0, -4, -2, 2, 2, 6, -2, -2, -6, 6, -6, 0, 0, 0, 0, 6, -6, 2, -2, 2, 0, -2, -2, 0, 8, 0
Offset: 1

Views

Author

Paul Curtz, Aug 25 2008

Keywords

Comments

Do the absolute values cover A004275?

Links

Programs

  • Mathematica
    #[[4]]-#[[3]]-#[[2]]+#[[1]]&/@Partition[Prime[Range[200]],4,2] (* Harvey P. Dale, Oct 11 2020 *)

Extensions

Edited by R. J. Mathar, Feb 27 2009

A031368 Odd-indexed primes: a(n) = prime(2n-1).

Original entry on oeis.org

2, 5, 11, 17, 23, 31, 41, 47, 59, 67, 73, 83, 97, 103, 109, 127, 137, 149, 157, 167, 179, 191, 197, 211, 227, 233, 241, 257, 269, 277, 283, 307, 313, 331, 347, 353, 367, 379, 389, 401, 419, 431, 439, 449, 461, 467, 487, 499, 509, 523, 547, 563
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

Appeared as a puzzle in "Stickelers", a nationally distributed feature, by Terry Stickels, Sep 28 2006. - Franklin T. Adams-Watters, Sep 28 2006
Also every second prime starting with 2. - Cino Hilliard, Dec 02 2007
Central terms of the triangle in A005145. - Reinhard Zumkeller, Aug 05 2009

Links

Crossrefs

Cf. A000040, A031215 (even-indexed primes), A005408.
First differences are A155067.

Programs

  • Haskell
    a031368 = a000040 . ((subtract 1) . (* 2))
a031368_list = map a000040 [1, 3 ..]  -- Reinhard Zumkeller, Nov 25 2012
  • Magma
    [ NthPrime(2*n-1): n in [1..1000] ]; // Vincenzo Librandi, Apr 11 2011
  • Maple
    A031368 := n->ithprime(2*n-1): seq(A031368(n), n=1..100);
  • Mathematica
    Table[ Prime[ 2n -1], {n, 52}] (* Robert G. Wilson v, Dec 01 2013 *)
  • PARI
    a(n) = prime(2*n-1) \\ Jianing Song, Jun 03 2021

Formula

a(n) = A219603(n) / A000040(n). - Reinhard Zumkeller, Nov 25 2012

A348774 A348773(2*n+1).

Original entry on oeis.org

2, 6, 12, 18, 24, 32, 42, 48, 60, 68, 74, 84, 98, 104, 110, 128, 138, 150, 158, 168, 180, 192, 198, 212, 228, 234, 242, 258, 270, 278, 284, 308, 314, 332, 348, 354, 368, 380, 390, 402, 420, 432, 440, 450, 462, 468, 488, 500, 510, 524, 548, 564, 572, 588, 600, 608, 618, 632, 644, 654
Offset: 0

Views

Author

N. J. A. Sloane, Nov 07 2021

Keywords

Comments

The first differences are 4, 6, 6, 6, 8, ... and apart from the initial term4, appears to coincide with A155067, the differences between successive odd-indexed primes. If confirmed, this will be one of the few formulas known for A307720.
The other bisection of A348773, A348775, seems much more mysterious.

Links

Crossrefs

Cf. A155067, A307720, A307730, A307632, A348773, A348775.

A155750 First differences of A031215.

Original entry on oeis.org

4, 6, 6, 10, 8, 6, 10, 8, 10, 8, 10, 12, 6, 6, 18, 8, 12, 12, 10, 8, 12, 6, 24, 6, 10, 12, 12, 8, 10, 12, 18, 6, 20, 12, 10, 14, 10, 14, 12, 12, 12, 10, 14, 6, 16, 12, 12, 18, 20, 16, 12, 8, 16, 8, 12, 6, 22, 6, 12, 14, 10, 18, 18, 14, 10, 14, 12, 18, 22, 12, 6, 12, 18, 6, 18, 6, 24
Offset: 1

Views

Author

Paul Curtz, Jan 26 2009

Keywords

Comments

All terms are even. Do all even numbers (A005843) appear at least once?

Links

Crossrefs

Cf. A005843, A031215.
Cf. A001223, A031131, A110854, A155067.

Programs

  • Mathematica
    Table[Prime[2*n+2] - Prime[2 n], {n, 80}] (* G. C. Greubel, Jun 05 2021 *)
  • Sage
    [nth_prime(2*n+2) - nth_prime(2*n) for n in (1..80)] # G. C. Greubel, Jun 05 2021

Formula

a(n) = A001223(2n) + A001223(2n+1). - R. J. Mathar, Feb 27 2009
a(n) = A031131(2n). - R. J. Mathar, Feb 27 2009

Extensions

Edited and extended by R. J. Mathar, Feb 27 2009
Showing 1-4 of 4 results.

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

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