A211404 Numbers k such that the leading k digits of k^k in decimal form a prime or a probable prime.

65, 603, 12208, 18803, 18841, 25207, 46115, 49885

Offset

1,1

Comments

Search completed through k = 28900. a(1) = 65 occurs in A220454, the 65-digit right truncation of 65^65 being the only prime right truncation for 65 and no first right truncation for a smaller number than 65 being 65 or more digits.

Search completed through k = 50000. - David Radcliffe, Jun 04 2025

Links

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

Chris K. Caldwell and G. L. Honaker, Jr., 65, Prime Curios!

Mathematica

Select[Range[8, 1000], PrimeQ[FromDigits[Take[IntegerDigits[#^#], #]]] &] (* T. D. Noe, Feb 11 2013 *)

Prog

(Python)
from gmpy2 import digits, is_prime, mpz
def ok(k): return is_prime(mpz(digits(k**k)[:k]))
print([k for k in range(1, 1000) if ok(k)]) # Michael S. Branicky, Jul 06 2025

Crossrefs

Cf. A000312, A220453, A220454.

Sequence in context: A286612 A276963 A338413 * A297317 A224099 A220229

Adjacent sequences: A211401 A211402 A211403 * A211405 A211406 A211407

Keyword

nonn,base,more

Author

James G. Merickel, Feb 09 2013

Extensions

a(7)-a(8) from David Radcliffe, Jun 04 2025

a(7) corrected by David Radcliffe, Jul 06 2025

Status

approved