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 1-2 of 2 results.

A290163 Primes p such that A288814(4*p) - A288814(3*p) = 7.

Original entry on oeis.org

2, 19, 29, 59, 79, 89, 131, 149, 151, 389, 479, 499, 521, 571, 631, 659, 701, 739, 919, 941, 971, 1069, 1279, 1289, 1361, 1381, 1451, 1471, 1489, 1669, 1949, 2069, 2089, 2131, 2549, 2609, 2749, 2791, 3011, 3109, 3181, 3251, 3361, 3389, 3539, 3581, 3659, 4049, 4091, 4139
Offset: 1

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Author

David James Sycamore, Jul 22 2017

Keywords

Comments

Proper subset of A290164.
Terms of A290164 not in this sequence include 5, 11, 61, 191, 431, 541, 1181, 3571, ... corresponding to primes p such that A(4*p) - A(3*p) = A(3*p) - 1, where A=A288814. Examples: A(4*5) - A(3*5) = 51 - 26 = 25; A(4*541) - A(3*541) = 6483 - 3242 = 3241.

Examples

			A288814(4*2) - A288814(3*2) = 15 - 8 = 7, therefore prime 2 is in the sequence;
A288814(4*19) - A288814(3*19) = 219 - 212 = 7, therefore prime 19 is a term.

Crossrefs

Cf. A259730, A288814, A290164.

Programs

  • Mathematica
    With[{s = Array[Boole[CompositeQ@ #] Total@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger[#]] &, 10^5]}, Select[Prime@ Range[600], Function[p, FirstPosition[s, ?(# == 4 p &)][[1]] - FirstPosition[s, ?(# == 3 p &)][[1]] == 7]]] (* Michael De Vlieger, Jul 23 2017 *)

Extensions

More terms from Altug Alkan, Jul 23 2017
Edited by Robert Israel, Jul 24 2017

A289556 Primes p such that both 5*p - 4 and 4*p - 5 are prime.

Original entry on oeis.org

3, 7, 13, 43, 67, 109, 127, 151, 163, 211, 277, 307, 373, 457, 463, 601, 613, 673, 727, 853, 919, 967, 1021, 1117, 1171, 1231, 1399, 1471, 1483, 1747, 1789, 1933, 2029, 2251, 2311, 2389, 2503, 2521, 2557, 2659, 2851, 2857, 3019, 3067, 3121, 3229, 3583, 3613, 3637, 3691, 3697
Offset: 1

Views

Author

David James Sycamore, Aug 02 2017

Keywords

Comments

The terms of this sequence belong to two disjoint subsequences, namely those for which |A(5*p) - A(4*p)| = 9; (3,7,13,43,67,127,163,211,277,307,457,...), and those for which 5*A(4*p) - 3*A(5*p) = 3, (109,151,373,673,919,...), where A = A288814.
Note: A288814(n) = A056240(n) for all composite n.

Examples

			P=7: 5*7 - 4 = 31, 4*7 - 5 = 23, both prime so 7 is in this sequence, and belongs to the subsequence of terms satisfying A(4*p) - A(3*p) = 9.
P=109: 5*109 - 4 = 541, 4*109 - 5 = 431, both prime so 109 is in this sequence, and belongs to the subsequence of terms satisfying 5*A(4*p) - 3*A(5*p) = 3.

Crossrefs

Cf. A259730, A288814, A290163, A290164, A056240.
Intersection of A136051 and A156300. - Michel Marcus, Aug 04 2017

Programs

  • Mathematica
    Select[Prime@ Range@ 516, Times @@ Boole@ Map[PrimeQ, {5 # - 4, 4 # - 5}] > 0 &] (* Michael De Vlieger, Aug 02 2017 *)

Extensions

More terms from Altug Alkan, Aug 02 2017
Showing 1-2 of 2 results.

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

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