A100904 -id:A100904

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A364077

Numbers k such that (12^k + 1)^2 - 2 is prime.

+10
3

1, 2, 8, 60, 513, 1047, 7021, 7506, 78858

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Such primes are sometimes called Kynea primes of base 12.

LINKS

Table of n, a(n) for n=1..9.

Prime-Wiki, Carol-Kynea prime.

Eric Weisstein's World of Mathematics, Near-Square Prime.

PROG

(PARI) for(k=1, 1200, ispseudoprime((12^k+1)^2-2)&&print1(k, ", "))

CROSSREFS

Cf. A091513 (b=2), A100902 (b=6), A100904 (b=10), A100906 (b=14), A364079 (b=18), A364081 (b=20), A100908 (b=22).

Cf. A364076.

KEYWORD

nonn,hard,more

AUTHOR

Jeppe Stig Nielsen, Jul 03 2023

STATUS

approved

A364079

Numbers k such that (18^k + 1)^2 - 2 is prime.

+10
3

1, 10, 21, 25, 31, 1083, 40485, 82516

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Such primes are sometimes called Kynea primes of base 18.

LINKS

Table of n, a(n) for n=1..8.

Prime-Wiki, Carol-Kynea prime.

Eric Weisstein's World of Mathematics, Near-Square Prime.

PROG

(PARI) for(k=1, 1200, ispseudoprime((18^k+1)^2-2)&&print1(k, ", "))

CROSSREFS

Cf. A091513 (b=2), A100902 (b=6), A100904 (b=10), A364077 (b=12), A100906 (b=14), A364081 (b=20), A100908 (b=22).

Cf. A364078.

KEYWORD

nonn,hard,more

AUTHOR

Jeppe Stig Nielsen, Jul 03 2023

STATUS

approved

A364081

Numbers k such that (20^k + 1)^2 - 2 is prime.

+10
3

1, 15, 44, 77, 141, 208, 304, 1169, 3359, 5050, 22431, 34935, 92990

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Such primes are sometimes called Kynea primes of base 20.

LINKS

Table of n, a(n) for n=1..13.

Prime-Wiki, Carol-Kynea prime.

Eric Weisstein's World of Mathematics, Near-Square Prime.

PROG

(PARI) for(k=1, 1200, ispseudoprime((20^k+1)^2-2)&&print1(k, ", "))

CROSSREFS

Cf. A091513 (b=2), A100902 (b=6), A100904 (b=10), A364077 (b=12), A100906 (b=14), A364079 (b=18), A100908 (b=22).

Cf. A364080.

KEYWORD

nonn,hard,more

AUTHOR

Jeppe Stig Nielsen, Jul 03 2023

STATUS

approved

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