A322094 a(n) = number of occurrences of the decimal representation of n in the concatenation of all terms preceding a(n), or n if there are no such occurrences.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 1, 24, 25, 26, 27, 28, 29, 30, 1, 32, 33, 1, 35, 36, 37, 38, 39, 40, 1, 1, 43, 44, 1, 46, 47, 48, 49, 50, 1, 1, 1, 54, 55, 1, 57, 58, 59, 60, 1, 1, 1, 1, 65, 66, 1, 68, 69, 70, 1, 1

Offset

1,2

Comments

In the definition of the sequence, consider the number of occurrences of string s in string t to be the number of positions within t that have a perfect match with the digits in s. Thus the number of occurrences of 11 in 1111 is 3 and not 2.

Links

John Mason, Table of n, a(n) for n = 1..10000

Example

a(12) is 1 as there is one occurrence of "12" in the string formed by concatenating a(1) through a(11).

Mathematica

FromDigits /@ Nest[Function[{a, n}, Append[a, If[# == 0, IntegerDigits@ n, IntegerDigits@ #] &@ SequenceCount[Join @@ a, IntegerDigits@ n]]] @@ {#, Length@ # + 1} &, {{1}}, 67] (* Michael De Vlieger, Nov 26 2018 *)

Crossrefs

Cf. A048991, A048992.

Sequence in context: A190600 A053832 A345672 * A056961 A297239 A043271

Adjacent sequences: A322091 A322092 A322093 * A322095 A322096 A322097

Keyword

nonn,base

Author

John Mason, Nov 26 2018

Status

approved