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

1,2

Links

Table of n, a(n) for n=1..80.

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

Example

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.

Prog

(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}

Crossrefs

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

Sequence in context: A127388 A307032 A273859 * A117332 A368578 A242704

Adjacent sequences: A332070 A332071 A332072 * A332074 A332075 A332076

Keyword

nonn

Author

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

Status

approved