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%I #20 Aug 01 2019 08:11:36
%S 3,4,6,7,8,12,15,18,22,24,30,70
%N 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.
%C 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".
%D F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 93, 1983.
%H Paul Erdős, <a href="http://www.jstor.org/stable/2689472">A Property of 70</a>, Mathematics Magazine, Vol. 51, No. 4 (Sep., 1978), pp. 238-240
%H Paul Erdős, D. E. Penney, and Carl Pomerance, <a href="http://dx.doi.org/10.1016/0022-314X(78)90018-5">On a class of relatively prime sequences</a>, Journal of Number Theory, Volume 10, Issue 4, November 1978, Pages 451-474.
%t (* This is only a recomputation of the sequence within its bounds. *)
%t 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]];
%t Select[Range[3, 70], okQ] (* _Jean-François Alcover_, Aug 01 2019 *)
%K nonn,fini,full,nice
%O 1,1
%A _Michel Marcus_, Mar 19 2014
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