A332177 The digitsum of a(n) is the product of the digits of a(n+1).

0, 10, 1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 25, 71, 24, 23, 51, 32, 115, 117, 33, 61, 171, 91, 52, 711, 133, 1117, 125, 42, 116, 81, 313, 1171, 152, 118, 215, 124, 1711, 251, 142, 7111, 512, 181, 521, 214, 111117, 26, 222, 123, 132, 161, 241, 111171, 34, 111711, 43, 117111, 62, 412

Offset

1,2

Comments

This is the lexicographically earliest infinite sequence of distinct nonnegative terms with this property; a(1) and a(2) are the only terms containing a zero.

Links

Carole Dubois, Table of n, a(n) for n = 1..1342

Example

a(20) = 19 and a(21) = 25; the digitsum of 19 is 10 and 10 is 2*5;
a(21) = 25 and a(22) = 71; the digitsum of 25 is 7 and 7 is 7*1;
a(22) = 71 and a(23) = 24; the digitsum of 71 is 8 and 8 is 2*4;
a(23) = 24 and a(25) = 23; the digitsum of 24 is 6 and 6 is 2*3; etc.

Prog

(Magma) a:=[0, 10]; for m in [3..70] do k:=1; while k in a or (IsPrime(&+Intseq(k)) and &+Intseq(k) ge 11) or &*Intseq(k) ne &+Intseq(a[m-1]) do k:=k+1; end while; Append(~a, k); end for; a; // Marius A. Burtea, Oct 16 2020

Crossrefs

Cf. A330521.

Sequence in context: A317330 A238880 A340138 * A130858 A098760 A107408

Adjacent sequences: A332174 A332175 A332176 * A332178 A332179 A332180

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Oct 02 2020

Status

approved