OFFSET
1,1
COMMENTS
Numbers n>9 with following property: form a sequence b(i) whose initial term is digit-product(n). Later terms are given by the rule that b(i) = b(i-1) + digit-product(b(i-1)) and n itself appears in the sequence.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
FORMULA
b(i) = b(i-1) + digit-product(b(i-1)).
EXAMPLE
The digit-product sequence for 22 begins with digit-product(22)= 4, 4 + 4 = 8, 8 + 8 = 16, 16 + 6 = 22. Since this procedure returns to the initial number 22, it belongs here.
The digit-product sequence for 102 begins with 2, 2 + 2 = 4, 4 + 4 = 8, 8 + 8 = 16, 16 + 6 = 22, 22 + 4 = 26, 26 + 12 = 38, 38 + 24 = 62, 62 + 12 = 74, 74 + 28 = 102. Since this procedure returns to the initial number 102, it belongs here.
PROG
(PARI) dp(n)=my(v=select(k->k>1, digits(n))); prod(i=1, #v, v[i])
is(n)=my(t=dp(n)); until(t>=n, t+=dp(t)); t==n \\ Charles R Greathouse IV, Jun 05 2014
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Anthony Sand, May 30 2014
STATUS
approved