A143833 -id:A143833 - cp's OEIS frontend

A143835 a(n) = Number of x <= 10^n such that 2x^2-1 is prime.

7, 45, 303, 2202, 17185, 141444, 1200975, 10448345, 92435171, 828797351, 7511268020, 68680339342

Offset: 1

Artur Jasinski, Sep 02 2008, Sep 04 2008

nonn

			a(1) = 7 because are 7 different x ={2, 3, 4, 6, 7, 8, 10} <= 10^1 where 2x^2-1 is prime = {7, 17, 31, 71, 97, 127, 199}.

Bernhard Helmes, Prime sieving on the polynomial f(n)=2n^2-1.

Cf. A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143832, A143833, A143834.

l = 0; p = 2; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], l = l + 1]; If[N[Log[x]/Log[10]] == Round[N[Log[x]/Log[10]]], Print[l]; AppendTo[a, l]], {x, 1, 10000000}]; a (*Artur Jasinski*)

Added link and extended to agree with website. - Ray Chandler, Jun 30 2015

A143832 Primes of the form 14 n^2-1.

Original entry on oeis.org

13, 223, 349, 503, 1399, 1693, 3583, 6173, 9463, 16183, 18143, 27103, 28349, 33613, 40823, 42349, 48733, 59149, 66653, 70573, 80863, 89599, 101149, 115933, 126349, 129023, 139999, 151423, 157303, 169399, 181943, 185149, 201599, 204973, 218749

Offset: 1

Artur Jasinski, Sep 02 2008

nonn

Primes of the form k n^2-1 k = 2 A066436 these n are A066049 k = 4 only one prime 3 when n = 1 k = 6 A090686 these n are A143826 k = 8 A090684 these n are A143827 k =10 A143828 these n are A143829 k =12 A143830 these n are A143831 k =14 A143832 these n are A143833 k =16 lack of primes

A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143833

p = 14; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, k]], {x, 1, 1000}]; a
Select[14*Range[200]^2-1,PrimeQ] (* Harvey P. Dale, Jul 29 2024 *)

A143834 Numbers k such that 2k^2 - 1 is not prime.

Original entry on oeis.org

1, 5, 9, 12, 14, 16, 19, 20, 23, 26, 27, 29, 30, 31, 32, 33, 35, 37, 40, 44, 47, 48, 51, 53, 54, 55, 57, 58, 60, 61, 65, 66, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 82, 83, 84, 86, 88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 110, 111, 114, 116, 117

Offset: 1

Artur Jasinski, Sep 02 2008

nonn

Complement of A066049.

Cf. A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143833.

[n: n in [1..120]| not IsPrime(2*n^2-1)] // Vincenzo Librandi, Jan 28 2011

p = 2; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k],NULL, AppendTo[a, x]], {x, 1, 1000}]; a
Select[Range[120],!PrimeQ[2#^2-1]&] (* Harvey P. Dale, Mar 14 2018 *)

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A143835 a(n) = Number of x <= 10^n such that 2x^2-1 is prime.

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A143832 Primes of the form 14 n^2-1.

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A143834 Numbers k such that 2k^2 - 1 is not prime.

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