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

1,1

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?

Links

Nicolas Bělohoubek, Table of n, a(n) for n = 1..900

Index entries for sequences related to decimal expansion of 1/n

Example

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).

Crossrefs

Sequence in context: A333379 A037015 A138218 * A359476 A070523 A350277

Adjacent sequences: A056052 A056053 A056054 * A056056 A056057 A056058

Keyword

nonn,base

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Status

approved