A217501 -id:A217501 - 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

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]

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]

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]

A221902 Primes of the form 2n^2 + 10n + 3.

Original entry on oeis.org

31, 103, 211, 751, 1291, 2371, 2803, 3271, 5503, 6151, 8311, 9103, 9931, 17851, 23971, 25303, 32503, 42331, 49603, 51511, 68071, 82003, 94603, 97231, 105331, 119551, 122503, 137803, 157351, 167611, 171103, 174631, 192811, 204151

Offset: 1

Vincenzo Librandi, Jan 31 2013

Conjecture: After the first term, 2^a(n)-1 is not prime; in other words, these primes (except 31) are included in A054723.

2*a(n) + 19 is a square. - Vincenzo Librandi, Apr 10 2015

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

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), A217621 (k=21).

Cf. A054723 (Prime exponents of nonprime Mersenne numbers).

[a: n in [1..500] | IsPrime(a) where a is 2*n^2 + 10*n + 3];

Select[Table[2 n^2 + 10 n + 3,{n, 500}],PrimeQ]

A221903 Primes of the form 2n^2 + 42n + 19.

Original entry on oeis.org

163, 811, 1423, 1783, 2179, 3079, 3583, 9739, 11503, 13411, 14419, 17659, 22483, 25111, 26479, 27883, 42139, 49411, 55243, 57259, 70111, 72379, 77023, 79399, 86743, 97039, 116443, 119359, 125299, 140779, 181603, 188911, 207811

Offset: 1

Vincenzo Librandi, Feb 01 2013

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

2*a(n) + 403 is a square. - Vincenzo Librandi, Apr 10 2015

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

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=9), 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).

Cf. A054723.

[a: n in [1..500] | IsPrime(a) where a is 2*n^2 + 42*n + 19];

Select[Table[2 n^2 + 42 n + 19, {n, 500}], PrimeQ]

cp's OEIS Frontend

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

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

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

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

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A221902 Primes of the form 2*n^2 + 10*n + 3.

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A221903 Primes of the form 2*n^2 + 42*n + 19.

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

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

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

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.

A221902 Primes of the form 2n^2 + 10n + 3.

A221903 Primes of the form 2n^2 + 42n + 19.