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A302021 Numbers k such that k^2+1, (k+2)^2+1 and (k+6)^2+1 are prime. 2
4, 14, 124, 204, 464, 1144, 1314, 1564, 1964, 2454, 3134, 4174, 4364, 5584, 5874, 6234, 7804, 8174, 8784, 9874, 9894, 10424, 12354, 12484, 12874, 14034, 14194, 15674, 16224, 18274, 18994, 21134, 21344, 22344, 22624, 23134, 23784, 23944, 24974, 25554, 26504, 26934, 27064, 27804, 29364 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..200 from Seiichi Manyama)

MAPLE

select(k->isprime(k^2+1) and isprime((k+2)^2+1) and isprime((k+6)^2+1), [$1..40000]); # Muniru A Asiru, Apr 02 2018

MATHEMATICA

Select[Range[1, 30000], PrimeQ[#^2 + 1] && PrimeQ[(# + 2)^2 + 1] && PrimeQ[(# + 6)^2 + 1] &] (* Vincenzo Librandi, Apr 02 2018 *)

PROG

(Python)

from python import isprime

k, klist, A302021_list = 0, [isprime(i**2+1) for i in range(6)], []

while len(A302021_list) < 10000:

    i = isprime((k+6)**2+1)

    if klist[0] and klist[2] and i:

        A302021_list.append(k)

    k += 1

    klist = klist[1:] + [i] # Chai Wah Wu, Apr 01 2018

(MAGMA) [n: n in [1..30000] | IsPrime(n^2+1) and IsPrime((n+2)^2+1) and IsPrime((n+6)^2+1)]; // Vincenzo Librandi, Apr 02 2018

(PARI) isok(k) = isprime(k^2+1) && isprime((k+2)^2+1) && isprime((k+6)^2+1); \\ Altug Alkan, Apr 02 2018

CROSSREFS

Cf. A005574, A096012, A302087.

Sequence in context: A240273 A137048 A137056 * A006824 A333730 A344201

Adjacent sequences:  A302018 A302019 A302020 * A302022 A302023 A302024

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 31 2018

STATUS

approved

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Last modified September 19 17:19 EDT 2021. Contains 347564 sequences. (Running on oeis4.)