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

Author

Eric Angelini, Sep 07 2023

Keywords

• base
• nonn

Comments

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

Examples

			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, ...
		

Links

• Eric Angelini, Same gaps pattern, Personal blog "Cinquante signes", Sept 2023.
• Eric Angelini, Same gaps pattern, Personal blog "Cinquante signes", Sept 2023. [Cached copy]

Crossrefs

Cf. A284516.

Programs

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 *)