

A342146


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


2



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
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OFFSET

1,1


COMMENTS

The terms come frequently in runs of consecutive integers. In particular, all intervals [10^k, ..., 10^k+(10^k1)/91], k >= 1, e.g., {10}, {100, ..., 110}, {1000, ..., 1110}, ..., are subsequences.
A342145 contains this as a subsequence.


LINKS

Table of n, a(n) for n=1..57.


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.


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^n1)/9), A005408 (odd numbers: 2n+1).
Sequence in context: A076364 A175223 A181698 * A048592 A190665 A242475
Adjacent sequences: A342143 A342144 A342145 * A342147 A342150 A342151


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Mar 01 2021


STATUS

approved



