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A292847 a(n) is the smallest odd prime of the form ((1 + sqrt(2n))^k) - (1 -  sqrt(2n))^k))/(2sqrt(2n)). 0
5, 7, 101, 11, 13, 269, 17, 19, 509, 23, 709, 821, 29, 31, 46957, 55399, 37, 168846239, 41, 43, 9177868096974864412935432937651459122761, 47, 485329129, 2789, 53, 3229, 3461, 59, 61, 1563353111, 139237612541, 67, 5021, 71, 73, 484639, 6221, 79, 6869, 83, 7549 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

When 2n + 3 = p is prime, a(n) = p.

LINKS

Table of n, a(n) for n=1..41.

EXAMPLE

For k = {1, 2, 3, 4, 5}, ((1 + sqrt(6))^k) - (1 - sqrt(6))^k))/(2sqrt(6)) = {1, 2, 9, 28, 101}. 101 is odd prime, so a(3) = 101.

MATHEMATICA

g[n_, k_] : = ((1 + Sqrt(n))^k) - (1 - Sqrt(n))^k))/(2Sqrt(n));

Table[n = 3; While[! PrimeQ[Expand@g[2n, k]], k++]; Expand@g[2n, k], {n, 41}]

CROSSREFS

Cf.A000129, A002605, A015518, A063727, A002532, A083099, A015519, A003683, A002534, A083102, A015520, A091914, A079773, A161007, A099134.

Sequence in context: A329006 A176619 A230379 * A088270 A259496 A267586

Adjacent sequences:  A292844 A292845 A292846 * A292848 A292849 A292850

KEYWORD

nonn

AUTHOR

XU Pingya, Sep 24 2017

STATUS

approved

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Last modified March 31 01:53 EDT 2020. Contains 333133 sequences. (Running on oeis4.)