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 A263450 Smallest integer k>0 such that there is at least one zero in the decimal representation of prime(n)^k. 1
 10, 10, 8, 4, 5, 6, 7, 4, 6, 4, 6, 3, 5, 3, 2, 2, 3, 5, 3, 2, 3, 3, 5, 3, 2, 1, 1, 1, 1, 4, 3, 3, 6, 4, 2, 2, 4, 3, 5, 4, 2, 4, 4, 3, 2, 2, 5, 3, 3, 3, 6, 4, 2, 2, 2, 4, 3, 3, 5, 3, 2, 4, 1, 3, 3, 2, 2, 6, 2, 2, 2, 4, 3, 5, 4, 6, 4, 2, 1, 1, 3, 4, 3, 5, 3, 3, 2, 2, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: there are an infinite number of ones in the sequence. Corresponding values of prime(n)^k: 1024, 59049, 390625, 2401, 161051, 4826809, 410338673, 130321 (not yet in OEIS). From Robert Israel, Oct 19 2015: (Start) By Dirichlet's theorem there are infinitely many n for which prime(n) == 1 (mod 100), and these all have a(n) = 1. All a(n) <= 20, since every x coprime to 10 has x^20 == 1 (mod 100). (End) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A071531(prime(n)). - Michel Marcus, Oct 21 2015 MAPLE f:= proc(m) local k; for k from 1 do      if has(convert(m^k, base, 10), 0) then return k fi    od end proc: seq(f(ithprime(i)), i=1..1000); # Robert Israel, Oct 19 2015 MATHEMATICA Reap[Do[p=Prime[n]; k=1; While[Min[IntegerDigits[p^k]]>0, k++]; Sow[k], {n, 1, 200}]][[2, 1]] PROG (PARI) a(n) = {p = prime(n); k = 1; while (vecmin(digits(p^k)), k++); k; } \\ Michel Marcus, Oct 21 2015 CROSSREFS Cf. A062584, A071531, A103662, A103663. Sequence in context: A276467 A112120 A099401 * A087028 A145279 A103708 Adjacent sequences:  A263447 A263448 A263449 * A263451 A263452 A263453 KEYWORD nonn,base AUTHOR Zak Seidov, Oct 18 2015 STATUS approved

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Last modified May 29 07:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)