A056055 Integers k > 1 such that the decimal expansion of 1/k contains k as a string. (If the decimal expansion terminates, trailing zeros do not count.)

3, 6, 7, 14, 17, 28, 58, 59, 83, 86, 87, 89, 97, 118, 167, 197, 228, 281, 313, 316, 339, 367, 379, 383, 456, 458, 469, 529, 541, 543, 569, 577, 587, 593, 607, 618, 626, 629, 647, 669, 673, 677, 678, 683, 687, 701, 709, 719, 722, 727, 729, 767, 771, 772, 778

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• nonn
• base

Comments

The sequence is probably infinite, since long-period primes (cf. A006883) especially with high first digit are likely candidates, but is there a proof? Does any k with finite expansion of 1/k (i.e., k = 2^j * 5^m) occur?

Examples

			118 is a term since 1/118 = 0.00847457627118... contains "118".
100 is not a term because 1/100 = 0.01 does not contain "100" (0.0100 does not count).
		

Links

• Nicolas Bělohoubek, Table of n, a(n) for n = 1..900
• Index entries for sequences related to decimal expansion of 1/n