A217494 -id:A217494 - cp's OEIS frontend

A176549 Primes of the form 2n^2+6n+1.

37, 109, 541, 757, 1009, 1297, 1621, 2377, 6841, 7561, 8317, 9109, 11701, 12637, 15661, 16741, 19009, 23977, 25309, 28081, 34057, 38917, 40609, 42337, 44101, 47737, 51517, 55441, 57457, 59509, 65881, 70309, 72577, 82009, 84457, 99901

Offset: 1

Vincenzo Librandi, Apr 20 2010

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

2*a(n) + 7 is a square. - Vincenzo Librandi, Apr 09 2015

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

Primes in A059993.
Subsequence of A093838.
Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): this sequence (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), A217621 (k=21).

[a: n in [0..300] | IsPrime(a) where a is 2*n^2+6*n+1]; // Vincenzo Librandi, Jul 26 2012

Select[Table[2 n^2 + 6 n + 1, {n, 2000}], PrimeQ] (* Vincenzo Librandi, Jul 26 2012 *)

Removed an obviously incorrect part of the definition - R. J. Mathar, Apr 21 2010

A217496 Primes of the form 2n^2 + 50n + 23.

Original entry on oeis.org

23, 131, 191, 911, 1223, 1451, 1571, 1823, 3323, 3671, 3851, 5651, 6323, 6791, 7523, 8291, 9371, 10223, 12671, 15731, 16091, 16823, 25931, 28751, 29723, 39191, 43223, 50591, 53831, 55823, 60611, 62723, 64151, 64871, 68531, 73823, 77723, 80111, 87491, 90023

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)+579 is a square. - Vincenzo Librandi, Mar 04 2013

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

Cf. A054723, A176549, A217494.

Subsequence of A002145.

[a: n in [0..200] | IsPrime(a) where a is 2*n^2 + 50*n + 23];

Select[Table[2 n^2 + 50 n + 23, {n, 0, 500}], PrimeQ]

A217497 Primes of the form 2n^2 + 54n + 25.

Original entry on oeis.org

421, 673, 2473, 4561, 5821, 9601, 12301, 14281, 19861, 30661, 32173, 33721, 61261, 67741, 84121, 94273, 107773, 110581, 122173, 134341, 170773, 203821, 207673, 223441, 227473, 265381, 274201, 287701, 344941, 365173, 391273, 396601, 418273, 423781, 469141

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) + 679 is a square. - Vincenzo Librandi, Apr 10 2015
Equivalently, primes of the form 36*n^2 + 36*n + 9. - Charles R Greathouse IV, Jul 24 2024

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

Subsequence of A002144.

Cf. A054723, A176549, A217494.

[a: n in [1..500] | IsPrime(a) where a is 2*n^2+54*n+25];

Select[Table[2 n^2 + 54 n + 25, {n, 500}], PrimeQ]

list(lim)=my(v=List()); for(n=2,(sqrtint(lim\1*2+679)-27)\6, my(p=18*n^2 + 162*n + 25); if(isprime(p), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jul 24 2024

a(n) >> n^2 log n. - Charles R Greathouse IV, Jul 24 2024

A217498 Primes of the form 2n^2 + 58n + 27.

Original entry on oeis.org

151, 367, 619, 907, 1231, 1987, 2887, 3391, 3931, 4507, 5119, 6451, 7927, 8719, 9547, 11311, 13219, 15271, 17467, 21031, 22291, 24919, 27691, 29131, 32119, 35251, 36871, 41947, 43711, 55051, 59119, 63331, 76831, 81619, 84067, 89071, 94219, 96847, 104947

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) + 787 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 A002145.

[a: n in [1..500] | IsPrime(a) where a is 2*n^2+58*n+27];

Select[Table[2 n^2 + 58 n + 27, {n, 500}], PrimeQ]

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

Original entry on oeis.org

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]

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]

cp's OEIS Frontend

A176549 Primes of the form 2*n^2+6*n+1.

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A217496 Primes of the form 2*n^2 + 50*n + 23.

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A217497 Primes of the form 2*n^2 + 54*n + 25.

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A217498 Primes of the form 2*n^2 + 58*n + 27.

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

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

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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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A176549 Primes of the form 2n^2+6n+1.

A217496 Primes of the form 2n^2 + 50n + 23.

A217497 Primes of the form 2n^2 + 54n + 25.

A217498 Primes of the form 2n^2 + 58n + 27.

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.