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A239458
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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.
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0
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3, 4, 6, 7, 8, 12, 15, 18, 22, 24, 30, 70
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OFFSET
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1,1
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COMMENTS
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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".
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REFERENCES
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F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 93, 1983.
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LINKS
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Paul Erdős, A Property of 70, Mathematics Magazine, Vol. 51, No. 4 (Sep., 1978), pp. 238-240
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MATHEMATICA
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(* 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]];
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CROSSREFS
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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STATUS
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approved
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