A243140 Numbers n such that n appears in the sequence beginning with the digit-product of n and extended by adding successive digit-products.

22, 26, 38, 55, 62, 88, 95, 102, 104, 108, 116, 122, 126, 138, 162, 174, 202, 206, 218, 234, 258, 410, 414, 430, 442, 474, 586, 826, 922, 1318, 1342, 1366, 1474, 1586, 1826, 1922, 1958, 2318, 2366, 2582, 2742, 3174, 3258, 3498, 4362

Offset: 1

Author

Anthony Sand, May 30 2014

Keywords

• nonn
• base

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.

The function digit-product(n) multiplies all nonzero digits of n (A051801). For example, digit-product(1230) = 1 * 2 * 3 = 6. The resultant sequence appears in A063114, n + product of nonzero digits of n.

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007629, A243021, A051801, A063114.

Programs

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

Formula

b(i) = b(i-1) + digit-product(b(i-1)).