A343102 a(n) is the sum of the number of times the digits in n (without repetition) have appeared in the sequence.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 2, 2, 2, 2, 2, 2, 2, 2, 19, 11, 8, 8, 8, 8, 8, 8, 14, 9, 11, 8, 8, 0, 1, 0, 0, 0, 8, 2, 16, 11, 10, 1, 1, 1, 2, 1, 10, 3, 17, 19, 10, 1, 1, 0, 1, 1, 9, 4, 20, 26, 14, 3, 5, 3, 2, 3, 11, 6, 21, 30, 15, 6, 4, 3, 5, 1, 10, 5, 31, 42, 24, 16, 15, 14, 14, 10

Offset

0,11

Comments

The fixed points > 0 in the first one million terms are 10, 310, 341, 351, 514. It is likely no more exist.

Links

Table of n, a(n) for n=0..87.

Scott R. Shannon, Image of the terms for n=0..1000000. The green line is a(n) = n.

Example

a(0) to a(9) = 0 as the digits 0 to 9 have not appeared in the sequence.
a(10) = 10 as 1 has not appeared while 0 has appeared ten times, thus a(10) = 0 + 10 = 10.
a(11) = 1 as the repetitions of 1 in 11 are ignored, and 1 has appeared once in the sequence.
a(12) = 2 as 1 has appeared twice while 2 has not appeared, thus a(12) = 2 + 0 = 2.
a(20) = 19 as 2 has appeared eight times while 0 has appeared eleven times, thus a(20) = 8 + 11 = 19.
a(22) = 8 as the repetitions of 2 in 22 are ignored, and 2 has appeared eight times in the sequence.

Mathematica

Block[{a = {}, d = ConstantArray[0, 10]}, Do[AppendTo[a, Total@ Map[d[[If[# == 0, 10, #] ]] &, Union@ IntegerDigits[i]]]; Set[d, d + DigitCount[a[[i + 1]] ]], {i, 0, 87}]; a] (* Michael De Vlieger, Apr 05 2021 *)

Crossrefs

Cf. A343103 (count all digits in n), A326834, A004207, A309261, A331162.

Sequence in context: A174921 A010180 A109013 * A213790 A240962 A376301

Adjacent sequences: A343099 A343100 A343101 * A343103 A343104 A343105

Keyword

nonn,base,look

Author

Scott R. Shannon, Apr 05 2021

Status

approved