cp's OEIS Frontend

A094106 a(n) is the maximal length L of a "power floor prime" sequence, i.e., a sequence of the form floor(x^k), k = 1, 2, ..., L such that floor(x) = prime(n).

%I A094106 #13 Feb 16 2025 08:32:53
%S A094106 8,7,8,5,10,12,16,14,18,22,24,26,27,28,34,35,37,39,40,45,43,46,49,51,
%T A094106 55,57
%N A094106 a(n) is the maximal length L of a "power floor prime" sequence, i.e., a sequence of the form floor(x^k), k = 1, 2, ..., L such that floor(x) = prime(n).
%D A094106 Crandall and Pomerance, "Prime numbers, a computational perspective", p. 69, Research Problem 1.75.
%H A094106 C. Rivera, <a href="http://www.primepuzzles.net/problems/prob_042.htm">Problem 42</a>
%H A094106 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_227.htm">Puzzle 227</a>
%H A094106 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerFloorPrimeSequence.html">Power Floor Prime Sequence</a>
%e A094106 a(1)=8 because for x=111/47 the sequence [x^k], k=1,2,... 2,5,13,31,73,173,409,967,... starts with 8 primes and this is the maximum for any x with [x]=2. (Compare also A063636, though the rational number x = 1287/545 used there is not of minimal height!)
%Y A094106 Cf. A076255, A076357.
%K A094106 nonn,more
%O A094106 1,1
%A A094106 Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), May 02 2004
%E A094106 a(22) = 46 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Jun 03 2004
%E A094106 a(23) = 49 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Jun 27 2004
%E A094106 a(24) = 51 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Aug 08 2004
%E A094106 a(25) and a(26) from Michael Kenn (michael.kenn(AT)philips.com), Jan 03 2006, who says: To achieve this result I used a shared network of 37 computers over the Christmas holidays. The total calculation time was equivalent to slightly more than 1 CPU year of a P4 - 2.4GHz.