A099640 Primes with subscripts described in A098213.

2, 2, 2, 19, 113, 509, 2551, 19267, 75041, 753143, 4310819, 38238461, 307379717, 805592213, 13341291553

Offset

1,1

Comments

These primes are the smallest ones that introduce consecutive prime segments of length n, providing "maximum-diversity matrices". See A098213.

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = prime(A098213(n)). See explanations at A098213.

Example

For n = 7: prime list = {2551,2557,2579,2591,2593,2609,2617}, consecutive differences = {6,22,12,2,16,8}, 7 X 7 matrix = [{abs(p(i)-p(j))], C[7,2] = 21 distinct positive matrix entries: {2,6,8,12,14,16,18,22,24,26,28,30,34,36,38,40,42,52,58,60,66}.

Mathematica

a[n_] := Module[{v = Prime[Range[n]]}, While[CountDistinct@ Flatten@ Abs@ Outer[Plus, v, -v] - 1 != Binomial[n, 2], v = Join[v[[2 ;; -1]], {NextPrime[v[[-1]]]}]]; v[[1]]]; Array[a, 10] (* Amiram Eldar, Feb 23 2025 *)

Prog

(PARI) s(v) = {my(d = List()); for(i = 1, #v, for(j = 1, i-1, listput(d, abs(v[i] - v[j])))); #Set(d); }
a(n) = {my(v = primes(n), t = n*(n-1)/2, j = 1); while(s(v) != t, v[j] = nextprime(1 + if(j==1, v[n], v[j-1])); j++; if(j > n, j -= n)); v[j]; } \\ Amiram Eldar, Feb 23 2025

Crossrefs

Cf. A098213, A079007.

Sequence in context: A358633 A087238 A226935 * A140283 A067097 A260082

Adjacent sequences: A099637 A099638 A099639 * A099641 A099642 A099643

Keyword

nonn,more

Author

Labos Elemer, Oct 29 2004

Extensions

a(14)-a(15) from Amiram Eldar, Feb 23 2025

Status

approved