A341282 Numbers k such that there is no k-digit number m with the property that the binary expansion of m begins with the base-10 digits of m.

4, 7, 10, 13, 32, 35, 38, 41, 60, 63, 66, 69, 72, 91, 94, 97, 100, 119, 122, 125, 128, 131, 150, 153, 156, 159, 178, 181, 184, 187, 206, 209, 212, 215, 218, 237, 240, 243, 246, 265, 268, 271, 274, 277, 296, 299, 302, 305, 324, 327, 330, 333, 352, 355, 358, 361, 364, 383, 386, 389

Offset

1,1

Comments

This sequence is based on a problem proposed on the French math site Diophante.

Equivalently, numbers k such that A341281(k) = 0.

Links

Michel Marcus, Table of n, a(n) for n = 1..75

Diophante, A107, Binaire = décimal (in French).

Example

The 3-digit number 110 is such that 110_10 = 1101110_2 and 110 is the smallest 3-digit number whose binary expansion's first three digits is equal to its decimal expansion, so 3 is not a term.
There is no 4-digit number m whose binary expansion's first 4 digits are the base-10 digits of m. Indeed, the 5-digit integer 10010_10 = 10011100011010_2 is the smallest integer whose binary and decimal expansions coincide through the first 4 digits (1001), but 10010 is not a 4-digit number, hence 4 is a term.

Crossrefs

Cf. A181929, A305213, A341281, A342363 (first differences).

Sequence in context: A119256 A143454 A318774 * A065810 A123837 A125620

Adjacent sequences: A341279 A341280 A341281 * A341283 A341284 A341285

Keyword

nonn,base

Author

Bernard Schott, Feb 22 2021

Extensions

More terms from Michel Marcus, Feb 25 2021

Status

approved