A342147 Numbers m such that m + (m+1) = 2m + 1 shares at least one digit with m+1.

0, 9, 10, 11, 15, 20, 23, 30, 31, 36, 40, 48, 50, 52, 57, 60, 61, 70, 73, 78, 80, 86, 89, 90, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 115, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 130, 131, 135

Offset

1,2

Comments

The terms come frequently in runs of consecutive integers. In particular, all intervals [10^k-1, ..., 10^k+(10^k-1)/9], k >= 1, e.g., {9, 10, 11}, {99, 100, ..., 111}, {999, ..., 1111}, ..., are subsequences. For k > 1, the actual intervals are strictly larger than that, to the left: instead of 1, one can subtract 5*(10^(k-1)-1)/9.

A342145 contains this as a subsequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..5000

Mathematica

Select[Range[0, 150], Length[Intersection[IntegerDigits[2#+1], IntegerDigits[#+1]]]>0&] (* Harvey P. Dale, Dec 04 2024 *)

Prog

(PARI) select( is_A342147(n)=#setintersect(Set(digits(n+1)), Set(digits(2*n+1))), [0..199])

Crossrefs

Cf. A342145, A342146 (variants: 2n+1 shares a digit with {n,n+1} resp. n).

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

Sequence in context: A085514 A086446 A168042 * A045522 A054967 A227801

Adjacent sequences: A342144 A342145 A342146 * A342148 A342149 A342150

Keyword

nonn,base

Author

M. F. Hasler, Mar 01 2021

Status

approved