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

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, 30, 32, 33, 34, 19, 35, 36, 38, 39, 40, 42, 23, 44, 45, 46, 48, 49, 50, 51, 52, 29, 54, 55, 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

Offset: 1

Author

Eric Angelini and M. F. Hasler, May 19 2020

Keywords

• nonn

Examples

			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.
		

Links

• Eric Angelini, Yellow commas, pink, red, blue..., personal blog "Cinquante signes" on blogspot.com, May 17 2020
• Eric Angelini, Yellow commas, pink, red, blue..., personal blog "Cinquante signes" on blogspot.com, May 17 2020 [Cached copy]

Crossrefs

Cf. A197756 (the Yellow Comma sequence: count digits between odd terms).

Programs

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}