A342146 Numbers m such that m + (m+1) = 2*m + 1 shares at least one digit with m.

9, 10, 12, 15, 19, 24, 25, 29, 31, 36, 37, 39, 49, 50, 51, 52, 57, 59, 61, 62, 69, 71, 73, 74, 75, 78, 79, 81, 87, 89, 91, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 115, 119, 120, 121, 122, 123, 124, 125

Offset

1,1

Comments

The terms come frequently in runs of consecutive integers. In particular, all intervals [10^k, ..., 10^k+(10^k-1)/9-1], k >= 1, e.g., {10}, {100, ..., 110}, {1000, ..., 1110}, ..., are subsequences.

A342145 contains this as a subsequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

9 is in the sequence because 9 + 10 = 19 shares a digit with 9.
No smaller number has this property: 0 + 1 = 1, ..., 8 + 9 = 17 do not share a digit with 1, ..., 8, respectively; nor does 11 + 12 = 23 share a digit with 11.
So the next term is 12, sharing the digit '2' with 12 + 13 = 25, but not 13 (13 + 14 = 27), nor 14 (14 + 15 = 29), but 15 shares again a digit with 15 + 16 = 31.

Mathematica

Select[Range[200], Length[Intersection[IntegerDigits[#], IntegerDigits[ 2 #+1]]]> 0&] (* Harvey P. Dale, Dec 17 2021 *)

Prog

(PARI) select( is_A342146(n)=#setintersect(Set(digits(n)), Set(digits(2*n+1))), [0..199])

Crossrefs

Cf. A342145, A342147 (variants: 2n+1 shares a digit with {n,n+1} or n+1).

Cf. A002275 (repunits: (10^n-1)/9), A005408 (odd numbers: 2n+1).

Sequence in context: A076364 A175223 A181698 * A048592 A190665 A242475

Adjacent sequences: A342143 A342144 A342145 * A342147 A342148 A342149

Keyword

nonn,base

Author

M. F. Hasler, Mar 01 2021

Status

approved