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.

A144360 Primes of the form 8^k + 7. Also, primes of the form 64^m + 7.

Original entry on oeis.org

71, 262151, 1073741831, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023
Offset: 1

Views

Author

Reikku Kulon, Sep 18 2008

Keywords

Comments

k=2m, since for odd k, 8^k + 7 is divisible by 3.
Prime numbers p in A144242 such that p-1 is the fourth a-gonal and seventh b-gonal number for some a and b. Namely, a = (8^k+14)/6 and b = (8^k + 41)/21.
This sequence appears to be a subset of A144313.
The next term has 178 digits. - Harvey P. Dale, Sep 03 2015

Examples

			71 - 1 = 70 is the fourth triskaidecagonal number and seventh pentagonal number.

Links

Crossrefs

Cf. A000040, A000668, A144231, A144232, A144233, A144234, A144236, A144242, A144245, A144246, A144247, A144313.

Programs

  • Magma
    [a: n in [0..80] | IsPrime(a) where a is 8^n+7]; // Vincenzo Librandi, Aug 02 2017
  • Mathematica
    Select[64^Range[40]+7,PrimeQ] (* Harvey P. Dale, Sep 03 2015 *)

Formula

a(n) = A253211(A217381(n)). - Amiram Eldar, Jul 23 2025

Extensions

Edited by Max Alekseyev, Feb 17 2011

A144245 Prime numbers of the form 9^k +- 8.

Original entry on oeis.org

17, 73, 89, 6553, 6569, 4782961, 4782977, 3486784393, 3486784409, 31381059601, 1350851717672992097, 984770902183611232889, 381520424476945831628649898801, 969773729787523602876821942164080815560169, 145557834293068928043467566190278008218249525830565939618489
Offset: 1

Views

Author

Reikku Kulon, Sep 15 2008

Keywords

Links

Crossrefs

Cf. A000040, A000668, A144231, A144232, A144233, A144234, A144236, A144242.

Programs

  • Mathematica
    Select[Union[Flatten[#+{8,-8}&/@(9^Range[100])]],PrimeQ] (* Harvey P. Dale, Oct 24 2012 *)

Extensions

Two additional terms from Harvey P. Dale, Oct 24 2012

A144246 Prime numbers of the form 10^k +- 9.

Original entry on oeis.org

19, 109, 991, 1009, 10009, 99991, 9999991, 1000000009, 1000000000000000009, 10000000000000000000009, 999999999999999999999999999999991, 999999999999999999999999999999999999999999991, 1000000000000000000000000000000000000000000009
Offset: 1

Views

Author

Reikku Kulon, Sep 15 2008

Keywords

Comments

This sequence illustrates the base-n representation of numbers having the form n^k +- (n - 1).

Links

Crossrefs

Cf. A000040, A000668, A144231, A144232, A144233, A144234, A144236, A144242, A144245.

Programs

  • Mathematica
    Select[Sort[Flatten[Table[10^n+{9,-9},{n,50}]]],PrimeQ] (* Harvey P. Dale, Jul 22 2016 *)

Extensions

a(13) from Amiram Eldar, Jul 24 2025

A144247 Prime numbers of the form 11^k +- 10.

Original entry on oeis.org

131, 1321, 214358891, 505447028499293761, 5559917313492231491, 895430243255237372246521, 20796505671840591460586660430317517562942313712635618374571, 539407797827634189900210968137750826278309533633974732577186113975171
Offset: 1

Views

Author

Reikku Kulon, Sep 15 2008

Keywords

Comments

The next term is 18621820132595144528407508578788012958402726053563392593510831217730632927190897881.
The next larger term is 11^273 - 10 and there are no further terms for k < 1001.
It is conjectured that 131 is the only palindrome in the sequence.

Links

Crossrefs

Cf. A000040, A000668, A144231, A144232, A144233, A144234, A144236, A144242, A144245, A144246.
Showing 1-4 of 4 results.

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

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