

A239458


Define a sequence b(n) such that b(k) is the smallest integer greater than b(k1) and relatively prime to the product b(0)*b(1)*...b(k1). The current sequence lists the starting b(0)'s such that all b(k), for k>= 1, are primes or powers of primes.


0



3, 4, 6, 7, 8, 12, 15, 18, 22, 24, 30, 70
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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. 238240
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 451474.


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] (* JeanFrançois Alcover, Aug 01 2019 *)


CROSSREFS

Sequence in context: A002191 A108348 A085149 * A007370 A322376 A044813
Adjacent sequences: A239455 A239456 A239457 * A239459 A239460 A239461


KEYWORD

nonn,fini,full,nice


AUTHOR

Michel Marcus, Mar 19 2014


STATUS

approved



