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 A078970 Cycle of the inventory sequence (as in A063850) starting with n consists of prime numbers. 4
 39, 1319, 211319, 12311319, 41122319, 1431221319, 4114232219, 2431321319, 2214333119, 2231143319, 2233311419, 2233311419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It can be proved that any inventory sequence ends in a cycle all of whose terms are <= 10^20. LINKS Carlos Rivera, The Inventory Sequences and Self-Inventoried Numbers EXAMPLE The inventory sequence starting with 39 is: 39, 1319, 211319, 12311319, 41122319, 1431221319, 4114232219, 2431321319, 2214333119, 2231143319, 2233311419, 2233311419,.... The cycle is 2233311419, 2233311419, .... and 2233311419 is prime. MATHEMATICA g[n_] := Module[{seen, r, d, l, i, t}, seen = {}; r = {}; d = IntegerDigits[n]; l = Length[d]; For[i = 1, i <= l, i++, t = d[[i]]; If[ ! MemberQ[seen, t], r = Join[r, IntegerDigits[Count[d, t]]]; r = Join[r, {t}]; seen = Append[seen, t]]]; FromDigits[r]]; pr[n_] := Module[{r, t, p1, p, a}, r = {}; t = g[n]; a = True; While[ ! MemberQ[r, t], r = Append[r, t]; t = g[t]]; r = Append[r, t]; p1 = Flatten[Position[r, t]]; p = PrimeQ[Drop[r, p1[[1]]]]; If[MemberQ[p, False], a = False]; a]; l = {}; For[k = 1, k <= 10^4, k++, If[pr[k], l = Append[l, k]]] CROSSREFS Cf. A063850, A078786. Sequence in context: A227524 A240442 A009729 * A020303 A235973 A097314 Adjacent sequences:  A078967 A078968 A078969 * A078971 A078972 A078973 KEYWORD base,nice,nonn AUTHOR Joseph L. Pe, Jan 14 2003 STATUS approved

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Last modified August 10 04:38 EDT 2020. Contains 336368 sequences. (Running on oeis4.)