VOOZH about

URL: https://oeis.org/A078970

⇱ A078970 - OEIS


login
A078970
Cycle of the inventory sequence (as in A063850) starting with n consists of prime numbers.
4
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
1,1
COMMENTS
It can be proved that any inventory sequence ends in a cycle all of whose terms are <= 10^20.
LINKS
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, so 39 is in the sequence.
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
CROSSREFS
Sequence in context: A043245 A044025 A062668 * A158339 A211499 A126077
KEYWORD
base,nice,nonn
AUTHOR
Joseph L. Pe, Jan 14 2003
EXTENSIONS
Missing terms inserted by Sean A. Irvine, Jul 25 2025
STATUS
approved