A301522 -id:A301522 - cp's OEIS frontend

A301642 Primes of form 16*k^k + 1.

Original entry on oeis.org

17, 433, 746497, 142657607172097

Offset: 1

Seiichi Manyama, Mar 25 2018

nonn

The next term is too large to include.

The next term a(5) has 108 digits; a(6) has 166 digits; a(7) has 170 digits. - Harvey P. Dale, Aug 23 2019

Primes of form b*k^k + 1: A121270 (b=1), A216148 (b=2), A301644 (b=3), A301641 (b=4), this sequence (b=16).

Cf. A301522.

Select[Table[16*k^k+1,{k,20}],PrimeQ] (* Harvey P. Dale, Aug 23 2019 *)

a(n) = 16*A301522(n+1)^A301522(n+1) + 1.

A301519 Numbers k such that 4*k^k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 7, 25, 7143, 11583

Offset: 1

Seiichi Manyama, Mar 23 2018

a(9) > 20000, if it exists. All terms correspond to certified primes. - Giovanni Resta, Apr 06 2018

Cf. A110932, A160600, A301520, A301522.

Flatten[{0, Select[Range[1000], PrimeQ[4*#^# + 1] &]}] (* Vaclav Kotesovec, Mar 25 2018 *)

for(n=0, 100, if(isprime(4*n^n+1), print1(n", ")))

a(7)-a(8) from Giovanni Resta, Apr 06 2018

A301524 Numbers k such that 16*k^k - 1 is prime.

Original entry on oeis.org

3, 5, 15, 27

Offset: 1

Seiichi Manyama, Mar 23 2018

All terms are odd since 16*(2*m)^(2*m) - 1 = (2^(m+2)*m^m - 1)*(2^(m+2)*m^m + 1). - Altug Alkan, Mar 23 2018
a(5), if it exists, is greater than 5000. - Vaclav Kotesovec, Mar 25 2018
a(5), if it exists, is greater than 20000. - Michael S. Branicky, Sep 03 2024

Cf. A110931, A301522.

Select[Range[1000], PrimeQ[16*#^# - 1] &] (* Vaclav Kotesovec, Mar 25 2018 *)

for(n=0, 1000, if(isprime(16*n^n-1), print1(n", ")))

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A301642 Primes of form 16*k^k + 1.

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A301519 Numbers k such that 4*k^k + 1 is prime.

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A301524 Numbers k such that 16*k^k - 1 is prime.

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