The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A321871

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A321871

Numbers k such that m = 4k^2 + 2k + 17 and 4m - 3 are both primes.
(history; published version)

#13 by Hugo Pfoertner at Sat Jul 17 06:56:09 EDT 2021

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proposed

approved

#12 by Jon E. Schoenfield at Sat Jul 17 04:53:19 EDT 2021

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editing

proposed

#11 by Jon E. Schoenfield at Sat Jul 17 04:53:17 EDT 2021

NAME

Numbers n k such that m = 4n4k^2 + 2n 2k + 17 and 4m - 3 are both primes.

COMMENTS

Rotkiewicz proved that if n k is in this sequence, and m = 4n4k^2 + 2n 2k + 17, then m*(4m - 3) is a decagonal Fermat pseudoprime to base 2 (A321870), and thus under Schinzel's Hypothesis H there are infinitely many decagonal Fermat pseudoprimes to base 2.

EXAMPLE

1 is in the sequence since 4*1^2 + 2*1 + 17 = 23 and 4*23 - 3 = 89 are both primes.

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approved

editing

#10 by Sean A. Irvine at Thu Jul 25 00:13:01 EDT 2019

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proposed

approved

#9 by Amiram Eldar at Wed Jul 24 05:28:09 EDT 2019

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editing

proposed

#8 by Amiram Eldar at Wed Jul 24 05:24:50 EDT 2019

LINKS

Amiram Eldar, <a href="/A321871/b321871.txt">Table of n, a(n) for n = 1..10000</a>

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approved

editing

#7 by N. J. A. Sloane at Sat Dec 01 08:28:56 EST 2018

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proposed

approved

#6 by Michel Marcus at Tue Nov 20 09:32:39 EST 2018

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editing

proposed

#5 by Michel Marcus at Tue Nov 20 09:32:34 EST 2018

PROG

(PARI) isok(n) = isprime(m=4*n^2 + 2*n + 17) && isprime(4*m-3); \\ Michel Marcus, Nov 20 2018

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proposed

editing

#4 by Amiram Eldar at Tue Nov 20 06:38:42 EST 2018

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editing

proposed