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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A177679 Numbers k such that 30*k and 60*k are both the average of twin prime pairs.

Original entry on oeis.org

1, 22, 27, 71, 85, 111, 113, 195, 209, 351, 1106, 1387, 1471, 1785, 1848, 1911, 2128, 2170, 2346, 2366, 2409, 2470, 2492, 2626, 2689, 2731, 2918, 3108, 3410, 3849, 4159, 4466, 4565, 5214, 5382, 5615, 6117, 6161, 6559, 7035, 7063, 7349, 7469, 7798, 7923
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 10 2010

Keywords

Examples

			a(1)=1 because 30*1-1=29, 30*1+1=31, 60*1-1=59 and 60*1+1=61 are all twin primes.
		

Crossrefs

Cf. A014574.

Programs

  • Magma
    [k:k in [1..8000]|IsPrime(30*k-1) and IsPrime(30*k+1) and IsPrime(60*k-1) and IsPrime(60*k+1)]; // Marius A. Burtea, Dec 20 2019
  • Mathematica
    Select[Range[8000], AllTrue[{30#-1, 30#+1, 60#-1, 60#+1}, PrimeQ] &] (* Amiram Eldar, Dec 20 2019 *)

Formula

a(n) = A066388(n+1)/30.

Extensions

Corrected (185 replaced by 195, 2718 replaced by 2918, 2731 inserted etc.) by R. J. Mathar, May 15 2010

A177680 Numbers n such that 6n and 12n are both the average of twin prime pairs.

Original entry on oeis.org

1, 5, 110, 135, 355, 425, 555, 565, 975, 1045, 1755, 5530, 6935, 7355, 8925, 9240, 9555, 10640, 10850, 11730, 11830, 12045, 12350, 12460, 13130, 13445, 13655, 14590, 15540, 17050, 19245, 20795, 22330, 22825, 26070, 26910, 28075, 30585, 30805
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 10 2010

Keywords

Comments

Conjecture: all terms but the first term are multiples of 5. - Harvey P. Dale, Sep 26 2017

Examples

			a(1)=1 because 6*1-1=5, 6*1+1=7, 12*1-1=11 and 12*1+1=13 are all twin primes.
		

Crossrefs

Cf. A014574.

Programs

  • Mathematica
    Select[Range[31000],AllTrue[Flatten[{6*#+{1,-1},12*#+{1,-1}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 26 2017 *)

Formula

a(n)=A066388(n)/6.

Extensions

Corrected (13590 removed, 13655 and 14590 inserted, 22725 replaced by 22825) by R. J. Mathar, May 15 2010
Previous Showing 11-12 of 12 results.