A078970 Cycle of the inventory sequence (as in A063850) starting with n consists of prime numbers.
39, 93, 349, 394, 439, 493, 934, 943, 999, 1139, 1193, 1319, 1391, 1913, 1931, 1999, 3139, 3193, 3319, 3339, 3391, 3393, 3913, 3931, 3933, 9111, 9139, 9193, 9319, 9391, 9399, 9913, 9931, 9939, 9993, 11129, 11192, 11219, 11291, 11912, 11921, 12119, 12191, 12239
Offset: 1
Examples
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, so 39 is in the sequence.
Links
- Carlos Rivera, Puzzle 207. The Inventory Sequences and Self-Inventoried Numbers, The Prime Puzzles & Problems Connection.
Programs
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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]]]; l
Extensions
Missing terms inserted by Sean A. Irvine, Jul 25 2025
Comments