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).

8, 7, 8, 5, 10, 12, 16, 14, 18, 22, 24, 26, 27, 28, 34, 35, 37, 39, 40, 45, 43, 46, 49, 51, 55, 57

Offset: 1

Author

Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), May 02 2004

Keywords

• nonn
• more

Examples

			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!)
		

References

• Crandall and Pomerance, "Prime numbers, a computational perspective", p. 69, Research Problem 1.75.

Links

• C. Rivera, Problem 42
• C. Rivera, Puzzle 227
• Eric Weisstein's World of Mathematics, Power Floor Prime Sequence

Crossrefs

Cf. A076255, A076357.

Extensions

a(22) = 46 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Jun 03 2004

a(23) = 49 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Jun 27 2004

a(24) = 51 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Aug 08 2004

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.