A217494 -id:A217494 - cp's OEIS frontend

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

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

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

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

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

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cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

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.