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 1-3 of 3 results.

A154773 Numbers n such that 252n^2 is the average of a twin prime pair.

Original entry on oeis.org

3, 5, 11, 14, 18, 20, 26, 27, 28, 29, 31, 38, 42, 52, 58, 64, 73, 82, 85, 90, 110, 125, 138, 156, 167, 180, 212, 234, 248, 297, 299, 303, 305, 308, 312, 314, 317, 319, 334, 336, 348, 361, 365, 371, 372, 377, 379, 414, 451, 465, 478, 499, 508, 509, 535, 554, 564
Offset: 1

Views

Author

M. F. Hasler, Jan 15 2009

Keywords

Comments

Inspired by Zak Seidov's post to the SeqFan list, cf. link: This yields A154673 as 252 a(n)^2. Indeed, if N/7 is a square, then N=7m^2 and this can't be the average of a twin prime pair unless m=6a.

Links

Crossrefs

Cf. A037073, A154331, A154772.

Programs

  • Mathematica
    Select[Range[600],And@@PrimeQ[252#^2+{1,-1}]&] (* Harvey P. Dale, Dec 13 2012 *)
  • PARI
    for(i=1,999, isprime(252*i^2+1) & isprime(252*i^2-1) & print1(i","))

Formula

a(n) = sqrt(A154673(n)/252).

A154774 Numbers n such that 9900n^2 is the average of a twin prime pair.

Original entry on oeis.org

10, 14, 15, 25, 60, 74, 76, 87, 127, 129, 130, 140, 171, 196, 207, 224, 259, 263, 302, 314, 315, 319, 333, 337, 377, 389, 451, 454, 470, 491, 508, 518, 549, 568, 574, 589, 592, 624, 629, 636, 690, 696, 729, 748, 753, 769, 770, 771, 781, 791, 802, 833, 844
Offset: 1

Views

Author

M. F. Hasler, Jan 15 2009

Keywords

Comments

Inspired by Zak Seidov's post to the SeqFan list, cf. link: This yields A154674 as 9900 a(n)^2. Indeed, if N/11 is a square, then N=11 m^2 and this can't be the average of a twin prime pair unless m=30a (considering N+1 mod 2,3,5 and N-1 mod 5).

Links

Crossrefs

Cf. A037073, A154331, A154772-A154773.

Programs

  • Mathematica
    Select[Range[1000],AllTrue[9900#^2+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 19 2019 *)
  • PARI
    for(i=1,999, isprime(9900*i^2+1) & isprime(9900*i^2-1) & print1(i","))

Formula

a(n) = sqrt(A154674(n)/9900).

A154775 Numbers k such that 13*(6*k)^2 is the average of a twin prime pair.

Original entry on oeis.org

2, 4, 5, 42, 46, 49, 59, 82, 84, 100, 119, 128, 137, 182, 185, 187, 192, 233, 264, 301, 303, 340, 376, 390, 395, 422, 438, 446, 471, 472, 494, 518, 527, 570, 598, 609, 611, 633, 667, 688, 714, 716, 726, 728, 733, 744, 831, 837, 865, 875, 896, 926, 940, 948
Offset: 1

Views

Author

M. F. Hasler, Jan 15 2009

Keywords

Comments

Inspired by Zak Seidov's post to the SeqFan list, cf. link: This yields A154675 as 468 a(n)^2. Indeed, if N/13 is a square, then N=13 k^2 and this can't be the average of a twin prime pair unless k=6m.

Links

Crossrefs

Cf. A014574, A037073, A154331, A154772, A154773, A154774, A154675.

Programs

  • Mathematica
    okQ[n_]:=Module[{av=468n^2},PrimeQ[av-1]&&PrimeQ[av+1]]; Select[Range[1000],okQ] (* Harvey P. Dale, Jan 21 2011 *)
  • PARI
    for(i=1,999, isprime(468*i^2+1) & isprime(468*i^2-1) & print1(i","))

Formula

a(n) = sqrt(A154675(n)/468).
Showing 1-3 of 3 results.

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

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