A239458 Define a sequence b(n) such that b(k) is the smallest integer greater than b(k-1) and relatively prime to the product b(0)*b(1)*...b(k-1). The current sequence lists the starting b(0)'s such that all b(k), for k>= 1, are primes or powers of primes.

3, 4, 6, 7, 8, 12, 15, 18, 22, 24, 30, 70

Offset

1,1

Comments

Sequence defined by Paul Erdős in the referenced link, where he proves that "70 is the largest integer for which all the b(k) (for k >= 1) are primes or powers of primes".

References

F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 93, 1983.

Links

Table of n, a(n) for n=1..12.

Paul Erdős, A Property of 70, Mathematics Magazine, Vol. 51, No. 4 (Sep., 1978), pp. 238-240

Paul Erdős, D. E. Penney, and Carl Pomerance, On a class of relatively prime sequences, Journal of Number Theory, Volume 10, Issue 4, November 1978, Pages 451-474.

Mathematica

(* This is only a recomputation of the sequence within its bounds. *)
okQ[b0_] := Module[{b, j}, b[0] = b0; b[k_] := b[k] = For[j = b[k - 1] + 1, True, j++, If[CoprimeQ[j, Product[b[m], {m, 0, k - 1}]], Return[j]]]; AllTrue[Array[b, 10], PrimePowerQ]];
Select[Range[3, 70], okQ] (* Jean-François Alcover, Aug 01 2019 *)

Crossrefs

Sequence in context: A002191 A108348 A085149 * A007370 A322376 A376424

Adjacent sequences: A239455 A239456 A239457 * A239459 A239460 A239461

Keyword

nonn,fini,full,nice

Author

Michel Marcus, Mar 19 2014

Status

approved