A253601 Numbers such that the smallest exponent for n and n^k to have common digits is 3.

4, 9, 17, 18, 24, 29, 33, 34, 38, 39, 44, 54, 57, 58, 59, 62, 67, 72, 79, 84, 88, 94, 144, 158, 173, 194, 209, 212, 224, 237, 238, 244, 247, 253, 257, 259, 307, 313, 314, 333, 334, 338, 349, 353, 359, 377, 388, 404, 409, 424, 437, 444, 447, 449, 454, 459, 467

Offset: 1

Author

Michel Marcus, Jan 05 2015

Keywords

• nonn
• base

Examples

			4^2=16 has no digits in common with 4, but 4^3=64 has some, so 4 is in the sequence.
		

Links

• Iain Fox, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A103173, A189056, A253600, A253602.

Programs

PARI

a253600(n) = {sd = Set(vecsort(digits(n))); k=2; while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); k;}
isok(n) = a253600(n) == 3;

PARI

is(n) = my(d(k)=Set(digits(n^k))); !#setintersect(d(1), d(2)) && #setintersect(d(1), d(3)) \\ Iain Fox, Aug 07 2018