A144231 -id:A144231 - cp's OEIS frontend

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

71, 262151, 1073741831, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023

Offset: 1

Reikku Kulon, Sep 18 2008

nonn

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10

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

[a: n in [0..80] | IsPrime(a) where a is 8^n+7]; // Vincenzo Librandi, Aug 02 2017

Select[64^Range[40]+7,PrimeQ] (* Harvey P. Dale, Sep 03 2015 *)

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

Edited by Max Alekseyev, Feb 17 2011

A144232 Prime numbers of the form 4^k +- 3.

Original entry on oeis.org

7, 13, 19, 61, 67, 1021, 4093, 4099, 16381, 65539, 262147, 1048573, 4194301, 16777213, 268435459, 1073741827, 19342813113834066795298819, 19807040628566084398385987581, 83076749736557242056487941267521533, 5316911983139663491615228241121378301, 1427247692705959881058285969449495136382746621

Offset: 1

Reikku Kulon, Sep 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..35

Subset of A122834.

Cf. A000040, A000668, A144231.

Select[Flatten[Table[4^n+{3,-3},{n,100}]],PrimeQ]//Union (* Harvey P. Dale, Nov 13 2020 *)

a(20)-a(21) from Amiram Eldar, Jul 24 2025

A144233 Prime numbers of the form 5^k +- 4 for k >= 1.

Original entry on oeis.org

29, 3121, 15629, 78121, 9765629, 30517578121, 710542735760100185871124267578121, 413590306276513837435704346034981426782906055450439453121, 197215226305252951352932141320696557418301608777255751192569732666015629

Offset: 1

Reikku Kulon, Sep 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..15

Cf. A000040, A000668, A144231, A144232.

Select[Flatten[Table[5^n+{-4,4},{n,90}]],PrimeQ] (* Harvey P. Dale, Jan 26 2019 *)

More terms from Alois P. Heinz, Jul 14 2019

A144234 Prime numbers of the form 6^k +- 5.

Original entry on oeis.org

11, 31, 41, 211, 1291, 1301, 279941, 60466181, 78364164101, 101559956668421, 36845653286788892983291, 1326443518324400147398651, 7958661109946400884391941, 286511799958070431838109691, 174588755932389037098918153698611839369211, 6285195213566005335561053533150026217291781

Offset: 1

Reikku Kulon, Sep 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..32

Cf. A000040, A000668, A144231, A144232, A144233.

Select[Sort[Flatten[#+{5,-5}&/@(6^Range[50])]],PrimeQ] (* Harvey P. Dale, May 12 2015 *)

a(15)-a(16) from Amiram Eldar, Jul 23 2025

A144236 Prime numbers of the form 7^k +- 6.

Original entry on oeis.org

13, 43, 337, 349, 117643, 40353601, 33232930569607, 558545864083284001, 1341068619663964900801, 7730993719707444524137094401, 2651730845859653471779023381607, 256923577521058878088611477224235621321601, 4318114567396436564035293097707728087552248843

Offset: 1

Reikku Kulon, Sep 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..20

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

Select[Flatten[Table[7^k+{6,-6},{k,40}]],PrimeQ]//Sort (* Harvey P. Dale, Jul 07 2021 *)

a(12)-a(13) from Amiram Eldar, Jul 23 2025

A144242 Prime numbers of the form 8^k +- 7.

Original entry on oeis.org

71, 262151, 1073741831, 549755813881, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023

Offset: 1

Reikku Kulon, Sep 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..14

Cf. A000040, A000668, A104066, A144231, A144232, A144233, A144234, A144236.

Select[Sort[Flatten[Table[8^k+{7,-7},{k,90}]]],PrimeQ] (* Harvey P. Dale, Aug 08 2016 *)

a(8) from Amiram Eldar, Jul 24 2025

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

Reikku Kulon, Sep 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..21 (terms 1..20 from Harvey P. Dale)

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

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

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

Reikku Kulon, Sep 15 2008

nonn

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

Amiram Eldar, Table of n, a(n) for n = 1..25

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

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

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

Reikku Kulon, Sep 15 2008

nonn

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.

Amiram Eldar, Table of n, a(n) for n = 1..10

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

cp's OEIS Frontend

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

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A144232 Prime numbers of the form 4^k +- 3.

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A144233 Prime numbers of the form 5^k +- 4 for k >= 1.

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A144234 Prime numbers of the form 6^k +- 5.

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A144236 Prime numbers of the form 7^k +- 6.

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A144242 Prime numbers of the form 8^k +- 7.

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

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

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

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