cp's OEIS Frontend

A231433 The digits of a(n) and a(n+1) taken together are the digits of a prime; least permutation of the nonnegative integers with this property.

%I A231433 #21 Dec 23 2024 14:53:43
%S A231433 0,11,2,3,1,4,7,6,10,9,5,12,8,18,13,15,14,17,20,23,21,16,19,22,30,25,
%T A231433 27,26,29,24,31,28,33,32,35,36,34,37,39,38,41,42,43,45,47,44,51,40,49,
%U A231433 46,57,50,53,48,59,56,63,52,61,54,67,55,69,58,70,60,71,62,72
%N A231433 The digits of a(n) and a(n+1) taken together are the digits of a prime; least permutation of the nonnegative integers with this property.
%C A231433 The offset is zero to have a permutation.
%C A231433 Sequence A128280 is an "arithmetic" analog, where instead of concatenation of digits, the terms are added.
%C A231433 Sequences A228407 and A228410 are the variants where "prime" is replaced by "palindrome".
%H A231433 Lars Blomberg, <a href="/A231433/b231433.txt">Table of n, a(n) for n = 0..9999</a>
%H A231433 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-November/011856.html">Two make a prime</a>, Nov 09 2013
%e A231433 Start with a(0)=0. The least prime having this digit is 101, so a(1)=11. Since 0 cannot be used any more and 111 is not a prime, the least digit that can be added to get the digits of some prime (namely 211) is a(2)=2, then a(3)=3 yields 23, etc.
%e A231433 See also the link to Angelini's post.
%o A231433 (PARI)  {a=u=0;for(n=1,99,u+=1<<a;print1(a",");for(k=1,9e9,bittest(u,k)&&next;d=Vec(Str(a,k));for(p=0,(#d)!-1, isprime(eval(concat(t=vecextract(d, numtoperm(#d, p)))))&&t[1]>"0"&&(a=k)&&next(3))))}
%K A231433 nonn,base
%O A231433 0,2
%A A231433 _Eric Angelini_ and _M. F. Hasler_, Nov 09 2013