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A332073 The Silver Comma sequence: Differences of indices of prime terms gives back the sequence; lexicographically earliest such permutation of positive integers.

%I A332073 #11 Dec 21 2024 21:03:15
%S A332073 1,2,3,4,5,6,8,7,9,10,12,11,14,15,16,18,13,20,21,22,24,25,17,26,27,28,
%T A332073 30,32,33,34,19,35,36,38,39,40,42,23,44,45,46,48,49,50,51,52,29,54,55,
%U A332073 56,57,58,60,62,63,64,31,65,66,68,69,70,72,74,75,76,77,78,37,80,81,82,84,85,86,87,88,90,91,41
%N A332073 The Silver Comma sequence: Differences of indices of prime terms gives back the sequence; lexicographically earliest such permutation of positive integers.
%H A332073 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2020/05/yellow-commas-pink-red-blue.html">Yellow commas, pink, red, blue...</a>, personal blog "Cinquante signes" on blogspot.com, May 17 2020
%H A332073 Eric Angelini, <a href="/A332072/a332072.pdf">Yellow commas, pink, red, blue...</a>, personal blog "Cinquante signes" on blogspot.com, May 17 2020 [Cached copy]
%e A332073 The prime terms are at indices 2, 3, 5, 8, 12, 17, 23, 31, 38, 47, 57, 69, 80, 94, ...; first differences give 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 11, 14, ... = the sequence itself.
%o A332073 (PARI) upto(N)={local(U=[2]); my(a=Vec([1,2],N), i=1, L=2, nxt(p)=while(#U>1 && U[2]==U[1]+1, U=U[^1]); my(t=U[1]); until(if(p, t=nextprime(t+1), !isprime(t+=1)) && !setsearch(U,t),); U=setunion(U,[t]);t); for(n=3,N,a[n]=nxt(n-L==a[i] && i++ && L=n));a}
%Y A332073 Cf. A197756 (the Yellow Comma sequence: count digits between odd terms).
%K A332073 nonn
%O A332073 1,2
%A A332073 _Eric Angelini_ and _M. F. Hasler_, May 19 2020