A217428 Numbers of the form 2^r*19^s whose decimal representation contains each digit 0-9 a prime number of times.

611897345462967423035506688, 98653640312161724942079430255181824, 195052744758517664687371356106391552, 69210613747809022824201189555756335104, 401770033097538379880522919696423452672

Offset: 1

Author

James G. Merickel, Oct 05 2012

Keywords

• nonn
• base
• less

Comments

See the formula section for more data, and others in cross-reference for similar and motivation.

Examples

			2^55 * 19^8 has two copies of each of the digits 0, 1, 2, 7 and 9; three copies of each of 3, 4, 5 and 8; and five copies of the digit 6.  All smaller numbers of the required type have at least a digit counted 0, 1, or a composite number of times, so this is a(1).
		

Crossrefs

Cf. A217854, A217429, A217430, A217404, A217407, A217410, A217413, A217416, A217419, A217422, A217425, A217431.

Programs

Mathematica

nd = 50; mx = 10^nd; pr = Prime@Range@PrimePi@nd; pQ[n_] := Union[DigitCount@n, pr] == pr; Sort@ Select[Flatten@ Table[2^p 19^q, {p, Log[2, mx/19]}, {q, Log[19, mx/2^p]}], pQ] (* Giovanni Resta, Jan 16 2014 *)

Formula

A217431(n) = 2^A217429(n) * 19^A217430(n)