A096347 Least number with n preimages (or immediate predecessors) under f(n) = n + (product of nonzero digits of n).

1, 2, 12, 102, 116, 1098, 2072, 1014, 101134, 11014, 1011098, 1003525, 41021255, 210110985, 403130555, 481104655, 4401225555, 4811125555, 86413249555, 39011218055

Offset: 0

Author

Jason Earls, Jun 29 2004

Keywords

• base
• more
• nonn

Comments

First occurrence of k in A096972.

a(20) > 10^11. [From Donovan Johnson, Nov 22 2009]

Examples

			a(3)=102 because 102 is the least number with three direct predecessors, 66: 66+6*6 = 102, 74: 74+7*4 = 102, 101: 101+1*1 = 102.
		

References

• P. A. Loomis, An Introduction to Digit Product Sequences (see link).

Links

• P. A. Loomis, An Interesting Family of Iterated Sequences.
• P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151.
• P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy]
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A096972, A063108, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931.

Extensions

a(8) to a(11) from Klaus Brockhaus, Jul 07 2004

a(12) from Robert G. Wilson v, Jul 15 2004

a(13)-a(19) from Donovan Johnson, Nov 22 2009