A107006 -id:A107006 - cp's OEIS frontend

A135984 a(n) = 24(prime(n))+7.

55, 79, 127, 175, 271, 319, 415, 463, 559, 703, 751, 895, 991, 1039, 1135, 1279, 1423, 1471, 1615, 1711, 1759, 1903, 1999, 2143, 2335, 2431, 2479, 2575, 2623, 2719, 3055, 3151, 3295, 3343, 3583, 3631, 3775, 3919, 4015, 4159, 4303, 4351, 4591, 4639, 4735

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Cf. A107006, A124477, A135657, A135982, A135983.

Mathematica
```
Table[24*Prime[n] + 7, {n, 1, 100}]
```

A135985 Prime numbers of the form 24*p + 7 where p is prime.

Original entry on oeis.org

79, 127, 271, 463, 751, 991, 1039, 1279, 1423, 1471, 1759, 1999, 2143, 2719, 3343, 3583, 3631, 3919, 4159, 4591, 4639, 4783, 5503, 5743, 5791, 7039, 7951, 8623, 9103, 9199, 9343, 9631, 10111, 10399, 10639, 11071, 11119, 11503, 12511

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A107006, A124477, A135657, A135982, A135983, A135984.

select(t -> isprime(t) and isprime((t-7)/24), [seq(p,p=7..20000,24)]); # Robert Israel, Oct 16 2018

a = {}; Do[If[PrimeQ[24(Prime[n]) + 7], AppendTo[a, 24(Prime[n]) + 7]], {n, 1, 100}]; a

A139527 Numbers n such that numbers 24n+5 are primes.

Original entry on oeis.org

0, 1, 2, 4, 6, 7, 8, 11, 12, 13, 16, 19, 21, 23, 27, 28, 29, 32, 33, 34, 39, 42, 44, 46, 49, 51, 53, 54, 57, 62, 67, 68, 71, 72, 78, 79, 81, 82, 83, 86, 89, 92, 93, 96, 97, 98, 99, 103, 106, 109, 112, 114, 116, 118, 119, 121, 123, 134, 141, 142, 144, 147, 148, 149, 153, 154

Offset: 1

Artur Jasinski, Apr 25 2008

nonn

Numbers n such that:
24n+1 is prime see A111174, primes 24n+1 see A107008
24n+5 is prime see A139527, primes 24n+5 see A107003
24n+7 is prime see A139483, primes 24n+7 see A107006
24n+11 is prime A139528, primes 24n+11 see A107007
24n+13 is prime see A139529, primes 24n+13 see A139530
24n+17 is prime see A139531, primes 24n+17 see A107181
24n+19 is prime see A139532, primes 24n+19 see A141373
24n+23 is prime see A131210, primes 24n+23 see A134517

Harvey P. Dale, Table of n, a(n) for n = 1..1000

a = {}; Do[If[PrimeQ[24 n + 5], AppendTo[a, n]], {n, 0, 200}]; a
Select[Table[(Prime[n]-5)/24,{n,800}],IntegerQ] (* Harvey P. Dale, Feb 25 2016 *)

A290402 Primes congruent to {7, 17} mod 24.

Original entry on oeis.org

7, 17, 31, 41, 79, 89, 103, 113, 127, 137, 151, 199, 223, 233, 257, 271, 281, 353, 367, 401, 439, 449, 463, 487, 521, 569, 593, 607, 617, 631, 641, 727, 751, 761, 809, 823, 857, 881, 919, 929, 953, 967, 977, 991, 1039, 1049, 1063, 1087, 1097, 1193, 1217, 1231

Offset: 1

Arkadiusz Wesolowski, Aug 03 2017

nonn

All these primes do not divide any number of the form 3*2^k - 1. Therefore, they are not in A001915.

Cf. A001915, A107006, A107181.

[p: p in PrimesUpTo(1231) | p mod 24 in {7, 17}];

Select[Prime@Range[202], MemberQ[{7, 17}, Mod[#, 24]] &]

A107006 UNION A107181.

A135658 Nonprimes of the form 4x^2-4xy+7y^2.

Original entry on oeis.org

4, 15, 16, 24, 28, 36, 40, 55, 60, 63, 64, 87, 88, 96, 100, 112, 124, 132, 135, 144, 159, 160, 168, 175, 196, 216, 220, 231, 232, 240, 247

Offset: 1

Artur Jasinski, Nov 25 2007

nonn

Because 4x^2-4*x*y+7*y^2 = (2*x-y)^2+6*y^2, this is a subsequence of A002481. - R. J. Mathar, Jan 18 2021

Cf. A107006, A124477, A135657.

Do[Do[w = 4x^2 - 4x y + 7y^2; If[w > 0, If[PrimeQ[w],[null], AppendTo[a, w]]], {x, 0, 100}], {y, 0, 100}]; Union[a]

A256172 Primes of the form 6p + 1 with p prime that are also of the form x^2 + 27y^2 and congruent to 7 mod 24.

Original entry on oeis.org

31, 223, 439, 1399, 2383, 2767, 3343, 3463, 3607, 4567, 6079, 7927, 8167, 8287, 8719, 10159, 10663, 11959, 14503, 15559, 15727, 17383, 18223, 19087, 20743, 21487, 21559, 24007, 25639, 26647, 27103, 27583, 28807, 28879, 29167, 29599, 31183, 32359, 33343

Offset: 1

Arkadiusz Wesolowski, Jun 01 2015

nonn

a(n) divides 2^m - 1, where m = (a(n) - 7)/6 + 1.

Subsequence of A122094.

Cf. A014752, A051644, A107006.

A014752 INTERSECT A051644 INTERSECT A107006.

cp's OEIS Frontend

A135984 a(n) = 24(prime(n))+7.

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A135985 Prime numbers of the form 24*p + 7 where p is prime.

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Maple

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A139527 Numbers n such that numbers 24n+5 are primes.

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Mathematica

A290402 Primes congruent to {7, 17} mod 24.

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Magma

Mathematica

Formula

A135658 Nonprimes of the form 4x^2-4xy+7y^2.

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Mathematica

A256172 Primes of the form 6*p + 1 with p prime that are also of the form x^2 + 27*y^2 and congruent to 7 mod 24.

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Formula

A256172 Primes of the form 6p + 1 with p prime that are also of the form x^2 + 27y^2 and congruent to 7 mod 24.