cp's OEIS Frontend

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.

%I A365513 #18 Dec 21 2024 21:18:12
%S A365513 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,
%T A365513 19,28,30,23,29,31,37,32,41,43,47,33,34,53,59,61,35,36,67,38,71,39,73,
%U A365513 79,83,40,89,42,97,101,103,107,44,45,46,109,48
%N 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.
%C A365513 The nonprime integers and the prime numbers appear in their natural order.
%H A365513 Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2023/09/same-gaps-pattern.html">Same gaps pattern</a>, Personal blog "Cinquante signes", Sept 2023.
%H A365513 Eric Angelini, <a href="/A365513/a365513.pdf">Same gaps pattern</a>, Personal blog "Cinquante signes", Sept 2023. [Cached copy]
%e A365513 Sequence read as a succession of terms:
%e A365513   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, ...
%e A365513 The gaps between nonprime terms are of size:
%e A365513   0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...
%e A365513 Sequence read as a succession of digits:
%e A365513   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 2, 1, 4, 1, 1, 1, 5, 1, 6, ...
%e A365513 The gaps between nonprime digits are of size:
%e A365513   0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...
%t A365513 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 *)
%Y A365513 Cf. A284516.
%K A365513 base,nonn
%O A365513 1,3
%A A365513 _Eric Angelini_, Sep 07 2023