A372550 Primes such that the next 10 prime gaps are all distinct.

15919, 15923, 24113, 24517, 30509, 34883, 34897, 36107, 49201, 52747, 56249, 64927, 64937, 66107, 66109, 66191, 67247, 67261, 67271, 67273, 68147, 70639, 70657, 70663, 70667, 70687, 70709, 70717, 71549, 75797, 78317, 78929, 79979, 81083, 81101, 83701, 88301, 94117, 94603, 94613, 96497, 97609

Offset: 1

Author

Zak Seidov and Robert Israel, May 05 2024

Keywords

• nonn

Examples

			a(3) = 24113 is a term because it is prime, the next 10 primes are 24121, 24133, 24137, 24151, 24169, 24179, 24181, 24197, 24203, 24223, and the gaps between these 11 primes are 8, 12, 4, 14, 18, 10, 2, 16, 6, 20 which are all distinct.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A079007.

Programs

Maple

P:= [seq(ithprime(i),i=1..11)]:
R:= NULL: count:= 0:
while count < 100 do
  P:= [op(P[2..-1]),nextprime(P[-1])];
  if nops(convert(P[2..-1]-P[1..-2],set))=10 then
    count:= count+1; R:= R,P[1];
  fi
od:
R;

Mathematica

s = {};
Do[If[10 == Length[Union[Differences[Prime[Range[k, k + 10]]]]], AppendTo[s,
Prime[k]]], {k,, 10000}]; s