A328018 If n is the k-th number divisible by 7 or containing a digit 7 (in base 10) then a(n) = a(k) otherwise a(n) = n.

1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 3, 18, 19, 20, 4, 22, 23, 24, 25, 26, 5, 6, 29, 30, 31, 32, 33, 34, 1, 36, 8, 38, 39, 40, 41, 9, 43, 44, 45, 46, 10, 48, 11, 50, 51, 52, 53, 54, 55, 12, 13, 58, 59, 60, 61, 62, 2, 64, 65, 66, 15, 68, 69, 16, 3

Offset

1,2

Links

Table of n, a(n) for n=1..71.

David A. Corneth, Pari Program

Rens Reus, Python program illustrating the first 100 terms

Example

Let F be the sequence of integers divisible by 7 or containing a digit 7 (A092433) with offset 1.
Sequence starts with the positive integers S.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, ...
Replace all integers in S that are also in F with the index of occurrence in F. Doing this gives:
1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 3, 18, 19, 20, 4, 22, 23, 24, 25, 26, 5, 6, 29, 30, 31, 32, 33, 34, 7, 36, 8, 38, 39, 40, ...
At position 35, we see 7, which is the first element in F so we replace this 7 with 1. This gives:
1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 3, 18, 19, 20, 4, 22, 23, 24, 25, 26, 5, 6, 29, 30, 31, 32, 33, 34, 1, 36, 8, 38, 39, 40, ...
Keep replacing numbers in S that are also in F with the index of occurrence they have in F. That is: if s in S is F(i) then set replace s with i.

Mathematica

Block[{nn = 70, s}, s = Select[Range[nn], Or[Mod[#, 7] == 0, DigitCount[#, 10, 7] > 0] &]; Array[If[FreeQ[s, #], #, FirstPosition[s, #][[1]] ] &, nn]] (* Michael De Vlieger, Oct 17 2019 *)

Prog

(PARI) See Corneth link
(PARI) k=0; for (n=1, #(a=vector(71)), print1 (a[n]=if (n%7==0 || setsearch(Set(digits(n)), 7), a[k++], n) ", ")) \\ Rémy Sigrist, Nov 11 2019
(Python) # See Reus link

Crossrefs

Cf. A092433.

Sequence in context: A160377 A269165 A319655 * A242603 A106608 A255692

Adjacent sequences: A328015 A328016 A328017 * A328019 A328020 A328021

Keyword

nonn,base,easy

Author

Rens Reus and David A. Corneth, Oct 01 2019

Status

approved