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 A252984 a(0)=4. a(n) is the smallest number not in the sequence such that Sum_{k=1..n} a(k) divides Product_{k=1..n} a(k). 1
 4, 12, 8, 24, 6, 10, 16, 20, 25, 3, 7, 5, 22, 13, 1, 19, 14, 11, 27, 9, 17, 2, 29, 15, 21, 23, 28, 34, 30, 31, 18, 35, 33, 26, 32, 37, 36, 38, 39, 45, 42, 43, 40, 49, 41, 48, 46, 44, 47, 50, 51, 54, 55, 53, 52, 56, 57, 62, 61, 60, 64, 68, 67, 58, 63, 70, 69, 71, 65, 77, 66, 72, 74, 73, 59 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjectured to be a permutation of the natural numbers. LINKS MATHEMATICA f[lst_List] := Block[{k = 1, s = Plus @@ lst, p = Times @@ lst}, While[ MemberQ[lst, k] || Mod[p*k, s + k] > 0, k++]; Append[ lst, k]]; Nest[f, {3}, 75] (* Robert G. Wilson v, Jan 19 2015 *) PROG (PARI) v=[4]; print1(4, ", "); n=1; while(n<100, p=prod(i=1, #v, v[i]); if(p*n\(vecsum(v)+n)==p*n/(vecsum(v)+n)&&!vecsearch(vecsort(v), n), v=concat(v, n); print1(n, ", "); n=0); n++) CROSSREFS Cf. A127644. Sequence in context: A145046 A205849 A208855 * A084415 A156681 A231100 Adjacent sequences:  A252981 A252982 A252983 * A252985 A252986 A252987 KEYWORD nonn AUTHOR Derek Orr, Jan 17 2015 STATUS approved

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Last modified April 12 10:52 EDT 2021. Contains 342920 sequences. (Running on oeis4.)