A365513 Lexicographically earliest permutation of the nonnegative integers with the property that the successive sizes of the gaps between nonprime terms and the successive sizes of the gaps between nonprime digits show the same pattern.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, 18, 20, 21, 13, 22, 24, 25, 26, 17, 27, 19, 28, 30, 23, 29, 31, 37, 32, 41, 43, 47, 33, 34, 53, 59, 61, 35, 36, 67, 38, 71, 39, 73, 79, 83, 40, 89, 42, 97, 101, 103, 107, 44, 45, 46, 109, 48

Offset

1,3

Comments

The nonprime integers and the prime numbers appear in their natural order.

Links

Table of n, a(n) for n=1..63.

Eric Angelini, Same gaps pattern, Personal blog "Cinquante signes", Sept 2023.

Example

Sequence read as a succession of terms:
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, ...
The gaps between nonprime terms are of size:
  0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...
Sequence read as a succession of digits:
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 2, 1, 4, 1, 1, 1, 5, 1, 6, ...
The gaps between nonprime digits are of size:
  0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...

Mathematica

a[1]=0; a[n_]:=a[n]=(k=1; While[MemberQ[s=Array[a, n-1], k]||PrimeQ@k!= PrimeQ[Flatten[IntegerDigits/@Join[s, {k}]][[n]]], k++]; k); Array[a, 70] (* Giorgos Kalogeropoulos, Sep 07 2023 *)

Crossrefs

Cf. A284516.

Sequence in context: A278581 A191889 A091402 * A064817 A366378 A108549

Adjacent sequences: A365510 A365511 A365512 * A365514 A365515 A365516

Keyword

base,nonn

Author

Eric Angelini, Sep 07 2023

Status

approved