A189555 Numbers n such that x' = n has two solutions, where x' is the arithmetic derivative (A003415) of x.

10, 12, 14, 18, 20, 21, 28, 31, 38, 39, 45, 55, 61, 71, 81, 87, 101, 103, 111, 119, 123, 129, 131, 147, 183, 185, 199, 211, 213, 215, 241, 243, 255, 269, 291, 297, 299, 327, 339, 343, 351, 355, 359, 361, 363, 381, 395, 399, 401, 411, 421, 433, 439, 471, 493

Offset

1,1

Comments

Ufnarovski and Ahlander conjecture that this sequence, and any such sequence that has numbers n such that x' = n has k solutions, is infinite. See A098700 and A189481 for the k=0 and 1 cases. It appears that the only even terms here are 10, 12, 14, 18, 20, 28, and 38. The prime terms are in A189556.

References

See A003415.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003.

Formula

n such that A099302(n) = 2.

Crossrefs

Cf. A003415, A098700 (no solution), A099302, A189481 (1 solution).

Sequence in context: A092132 A088170 A329522 * A116612 A068502 A109959

Adjacent sequences: A189552 A189553 A189554 * A189556 A189557 A189558

Keyword

nonn

Author

T. D. Noe, Apr 24 2011

Status

approved