A054723 -id:A054723 - cp's OEIS frontend

A217499 Primes of the form 2n^2 + 70n + 33.

181, 433, 1801, 4933, 5581, 7741, 13033, 18433, 24733, 41761, 47161, 49033, 94033, 96661, 104761, 140401, 156781, 174061, 188533, 207433, 227233, 252181, 265141, 370081, 385741, 412561, 423541, 440281, 451621, 510481, 535033, 572941, 598933, 659521, 666433

Offset: 1

Vincenzo Librandi, Oct 09 2012

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

2*a(n) + 1159 is a square. - Vincenzo Librandi, Apr 10 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. A054723, A176549, A217494.

Subsequence of A002144.

[a: n in [1..600] | IsPrime(a) where a is 2*n^2+70*n+33];

Select[Table[2 n^2 + 70 n + 33, {n, 600}], PrimeQ]

A135977 Mersenne composites (A065341) with exactly 3 prime factors.

Original entry on oeis.org

536870911, 8796093022207, 140737488355327, 9007199254740991, 2361183241434822606847, 9444732965739290427391, 604462909807314587353087

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..42

Subsequence of A065341.

Cf. A000225, A054723, A134852, A135975, A135976, A135978, A135979, A344515.

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], c = FactorInteger[2^Prime[n] - 1]; d = Length[c]; If[d == 3, AppendTo[k, 2^Prime[n] - 1]]], {n, 1, 40}]; k

a(n) = 2^A344515(n) - 1. - Amiram Eldar, May 23 2021

A217495 Primes of the form 2n^2 + 46n + 21.

Original entry on oeis.org

769, 1381, 1741, 2137, 3037, 3541, 4657, 7321, 9697, 22441, 26437, 30757, 35401, 37021, 38677, 47497, 49369, 55201, 61357, 72337, 79357, 81769, 96997, 99661, 105097, 134437, 188869, 207769, 211657, 227569, 256801, 306301, 330241, 469237, 480937, 492781, 510817

Offset: 1

Vincenzo Librandi, Oct 09 2012

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

2*a(n)+487 is a square. - Vincenzo Librandi, Mar 04 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), this sequence (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), A217501 (k=18), A217620 (k=19), A217621 (k=21).
Cf. A054723.
Subsequence of A002144.

[a: n in [1..500] | IsPrime(a) where a is 2*n^2+46*n+21];

Select[Table[2 n^2 + 46 n + 21, {n, 500}], PrimeQ]

A217500 Primes of the form 2n^2 + 74n + 35.

Original entry on oeis.org

191, 863, 1091, 1871, 2963, 3491, 3863, 4451, 9011, 15731, 21191, 21611, 29363, 30851, 35531, 42863, 44651, 45863, 47711, 50231, 52163, 60251, 65963, 68171, 71171, 75011, 100151, 101051, 109331, 112163, 119891, 144611, 147863, 164663, 179951, 204791, 254963

Offset: 1

Vincenzo Librandi, Oct 09 2012

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

2*a(n) + 1299 is a square. - Vincenzo Librandi, Apr 09 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), this sequence (k=17), A217501 (k=18), A217620 (k=19), A217621 (k=21).
Cf. A054723.
Subsequence of A002145.

[a: n in [1..600] | IsPrime(a) where a is 2*n^2 + 74*n + 35];

Select[Table[2n^2 + 74n + 35, {n, 600}], PrimeQ]

A217501 Primes of the form 2n^2 + 78n + 37.

Original entry on oeis.org

37, 577, 1657, 2089, 2557, 3061, 4177, 4789, 5437, 6121, 6841, 8389, 12889, 17137, 18289, 19477, 21961, 27361, 36541, 38197, 41617, 45181, 47017, 48889, 54721, 56737, 58789, 74161, 78877, 83737, 88741, 91297, 93889, 96517, 99181, 113041, 121789, 124777

Offset: 1

Vincenzo Librandi, Oct 09 2012

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

2*a(n) + 1447 is a square. - Vincenzo Librandi, Apr 09 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), this sequence (k=18), A217620 (k=19), A217621 (k=21).
Cf. A054723.
Subsequence of A002144.

[a: n in [0..600] | IsPrime(a) where a is 2*n^2+78*n+37];

Select[Table[2 n^2 + 78 n + 37, {n, 0, 600}], PrimeQ]

A217620 Primes of the form 2n^2 + 82n + 39.

Original entry on oeis.org

211, 499, 823, 1579, 2011, 4099, 6043, 6763, 8311, 10903, 11839, 18211, 27283, 28723, 34843, 38119, 41539, 56659, 58711, 76423, 86143, 88663, 93811, 99103, 110119, 121711, 124699, 130783, 149899, 163363, 173839, 181003, 188311, 222979, 227011, 231079, 247711

Offset: 1

Vincenzo Librandi, Oct 09 2012

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

2*a(n) + 1603 is a square. - Vincenzo Librandi, Apr 09 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), A217501 (k=18), this sequence (k=19), A217621 (k=21).
Cf. A054723.
Subsequence of A002145.

[a: n in [1..600] | IsPrime(a) where a is 2*n^2+82*n+39];

Select[Table[2 n^2 + 82 n + 39, {n, 600}], PrimeQ]

A217621 Primes of the form 2n^2 + 90n + 43.

Original entry on oeis.org

43, 331, 2311, 3931, 7351, 8971, 18043, 19231, 23011, 31543, 33091, 37951, 46771, 50551, 58543, 60631, 81043, 133711, 149731, 173671, 188143, 226843, 251791, 296251, 310291, 319831, 364543, 385351, 395971, 412171, 417643, 439891, 474343, 540871, 625111, 631843

Offset: 1

Vincenzo Librandi, Oct 09 2012

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

2*a(n) + 1939 is a square. - Vincenzo Librandi, Apr 09 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), A217501 (k=18), A217620 (k=19), this sequence (k=21).

Subsequence of A002145.

[a: n in [0..700] | IsPrime(a) where a is 2*n^2+90*n+43];

Select[Table[2 n^2 + 90 n + 43, {n, 0, 700}], PrimeQ]

A135976 Mersenne composites (A065341) with exactly 2 prime factors.

Original entry on oeis.org

2047, 8388607, 137438953471, 2199023255551, 576460752303423487, 147573952589676412927, 9671406556917033397649407, 158456325028528675187087900671, 2535301200456458802993406410751

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..39
Wikipedia, Semiprime.

Subsequence of A065341.

Cf. A000225, A054723, A134852, A135975, A135977, A135978, A135979.

A135976 := proc(n) local i;
i := 2^(ithprime(n))-1:
if (nops(numtheory[factorset](i)) = 2) then
   RETURN (i)
fi: end: [ seq(A135976(n), n=1..26) ]; # Jani Melik, Feb 09 2011

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], c = FactorInteger[2^Prime[n] - 1]; d = Length[c]; If[d == 2, AppendTo[k, 2^Prime[n] - 1]]], {n, 1, 40}]; k

forprime(p=1, 1e2, if(bigomega(2^p-1)==2, print1(2^p-1, ", "))) \\ Felix Fröhlich, Aug 12 2014

a(n) = 2^A135978(n) - 1. - Amiram Eldar, May 23 2021

A135978 Primes p such that 2^p-1 has exactly 2 prime factors.

Original entry on oeis.org

11, 23, 37, 41, 59, 67, 83, 97, 101, 103, 109, 131, 137, 139, 149, 167, 197, 199, 227, 241, 269, 271, 281, 293, 347, 373, 379, 421, 457, 487, 523, 727, 809, 881, 971, 983, 997, 1061, 1063

Offset: 1

Artur Jasinski, Dec 09 2007

a(40)>=1277. - Amiram Eldar, Sep 29 2018

Cf. A000225, A065341, A054723, A134852, A135975, A135976, A135977.

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], c = FactorInteger[2^Prime[n] - 1]; d = Length[c]; If[d == 2, AppendTo[k, Prime[n]]]], {n, 1, 40}]; k

a(17)-a(37) from Arkadiusz Wesolowski, Jan 26 2012

a(38)-a(39) from Amiram Eldar, Sep 29 2018

A243888 Primes of the form 2n^2+26n+11.

Original entry on oeis.org

71, 107, 191, 239, 347, 1031, 1439, 1667, 1787, 2039, 2447, 2591, 3371, 3539, 5231, 5651, 5867, 6311, 7247, 9311, 9587, 10151, 11027, 11939, 12251, 14207, 14891, 19727, 20939, 21767, 23039, 27539, 30431, 34511, 36107, 39971, 41687, 46439, 47051, 56039, 56711

Offset: 1

Vincenzo Librandi, Jun 16 2014

Subsequence of A068231.
Conjecture: except 107, 2^a(n)-1 is not prime; in other words, these primes are included in A054723.
2*a(n) + 147 is a square. - Vincenzo Librandi, Apr 10 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A068231.

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A221902 (k=1), A154577 (k=2), A154592 (k=3), A154601 (k=4), this sequence (k=5), A243889 (k=6), A217494 (k=7), A243890 (k=8), A221903 (k=9), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A243891 (k=14), A243957 (k=15), A217499 (k=16), A217500 (k=17), A217501 (k=18), A217620 (k=19), A243958 (k=20), A217621 (k=21).

[a: n in [1..200] | IsPrime(a) where a is 2*n^2+26*n+11];

Select[Table[2 n^2 + 26 n + 11, {n, 800}], PrimeQ]

cp's OEIS Frontend

A217499 Primes of the form 2*n^2 + 70*n + 33.

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Magma

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A135977 Mersenne composites (A065341) with exactly 3 prime factors.

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Formula

A217495 Primes of the form 2*n^2 + 46*n + 21.

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Magma

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A217500 Primes of the form 2*n^2 + 74*n + 35.

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Magma

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A217501 Primes of the form 2*n^2 + 78*n + 37.

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Magma

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A217620 Primes of the form 2*n^2 + 82*n + 39.

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Magma

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A217621 Primes of the form 2*n^2 + 90*n + 43.

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Magma

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A135976 Mersenne composites (A065341) with exactly 2 prime factors.

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PARI

A217499 Primes of the form 2n^2 + 70n + 33.

A217495 Primes of the form 2n^2 + 46n + 21.

A217500 Primes of the form 2n^2 + 74n + 35.

A217501 Primes of the form 2n^2 + 78n + 37.

A217620 Primes of the form 2n^2 + 82n + 39.

A217621 Primes of the form 2n^2 + 90n + 43.

A243888 Primes of the form 2n^2+26n+11.