A160697 -id:A160697 - cp's OEIS frontend

A066049 Numbers n such that 2*n^2 - 1 is a prime.

2, 3, 4, 6, 7, 8, 10, 11, 13, 15, 17, 18, 21, 22, 24, 25, 28, 34, 36, 38, 39, 41, 42, 43, 45, 46, 49, 50, 52, 56, 59, 62, 63, 64, 69, 73, 76, 80, 81, 85, 87, 91, 92, 95, 98, 102, 108, 109, 112, 113, 115, 118, 125, 126, 127, 132, 134, 137, 140, 141, 143, 153, 154, 155

Offset: 1

N. J. A. Sloane, Jan 09 2002

nonn

It is conjectured that this sequence is infinite.

A066436 gives resulting primes p such that (p+1)/2 is square. - Ray Chandler

D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A028870, A066436, A090697, A091176, A110558.

Select[Range[200],PrimeQ[2#^2-1]&] (* Harvey P. Dale, Jun 14 2011 *)

{ n=0; for (m=1, 10^9, if (isprime(2*m^2 - 1), write("b066049.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 08 2009

a(n) = A090697(n)/2 = A110558(n)/4. - Ray Chandler, Sep 15 2005

a(n) = A160697(n+1). - Reinhard Zumkeller, May 24 2009

Extended by Ray Chandler, Sep 15 2005

A160696 Largest k such that k^2 divides prime(n)+1.

Original entry on oeis.org

1, 2, 1, 2, 2, 1, 3, 2, 2, 1, 4, 1, 1, 2, 4, 3, 2, 1, 2, 6, 1, 4, 2, 3, 7, 1, 2, 6, 1, 1, 8, 2, 1, 2, 5, 2, 1, 2, 2, 1, 6, 1, 8, 1, 3, 10, 2, 4, 2, 1, 3, 4, 11, 6, 1, 2, 3, 4, 1, 1, 2, 7, 2, 2, 1, 1, 2, 13, 2, 5, 1, 6, 4, 1, 2, 8, 1, 1, 1, 1, 2, 1, 12, 1, 2, 2, 15, 1, 1, 4, 6, 4, 2, 2, 10, 6, 1, 3, 2, 1, 2, 3, 2

Offset: 1

Reinhard Zumkeller, May 24 2009

nonn

A160697 and A160698 give record values and where they occur.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000188, A008864, A049097, A049098.

a(n) = core(prime(n)+1, 1)[2]; \\ Michel Marcus, Nov 06 2022

a(A049097(n)) = 1; a(A049098(n)) > 1;

a(n) = A000188(A008864(n)).

A160698 Where record values occur in A160696.

Original entry on oeis.org

1, 2, 7, 11, 20, 25, 31, 46, 53, 68, 87, 106, 118, 152, 163, 190, 204, 247, 344, 377, 418, 436, 474, 492, 516, 558, 580, 647, 669, 713, 816, 894, 975, 1003, 1028, 1179, 1300, 1392, 1526, 1561, 1695, 1768, 1917, 1952, 2069, 2177, 2343, 2601, 2643, 2769, 2812

Offset: 1

Reinhard Zumkeller, May 24 2009

nonn

A160697(n)=A160696(a(n)) and A160696(m) < A160697(n) for m

Essentially the same as A091176. [From R. J. Mathar, May 29 2009]

Showing 1-3 of 3 results.

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A066049 Numbers n such that 2*n^2 - 1 is a prime.

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A160696 Largest k such that k^2 divides prime(n)+1.

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A160698 Where record values occur in A160696.

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