1,1

It can be proved that any inventory sequence ends in a cycle all of whose terms are <= 10^20.

Carlos Rivera, The Inventory Sequences and Self-Inventoried Numbers

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.

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]]]

Cf. A063850, A078786.

Sequence in context: A028219 A014936 A009729 this_sequence A020303 A097314 A112617

Adjacent sequences: A078967 A078968 A078969 this_sequence A078971 A078972 A078973

base,nice,nonn

Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 14 2003