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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. 0
3, 4, 6, 7, 8, 12, 15, 18, 22, 24, 30, 70 (list; graph; refs; listen; history; text; internal format)
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
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 A044813
KEYWORD
nonn,fini,full,nice
AUTHOR
Michel Marcus, Mar 19 2014
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)