A060064 First subsequent, disjoint occurrence of n consecutive nonprimes.

4, 8, 14, 24, 32, 90, 114, 140, 182, 200, 212, 294, 318, 524, 888, 1070, 1130, 1328, 1638, 1670, 1952, 2180, 2478, 2972, 3138, 3272, 4298, 4832, 5352, 5592, 8468, 9552, 9974, 12854, 14108, 15684, 16142, 19334, 19610, 25472, 28230, 31398, 31908, 34062

Offset: 1

Author

Jason Earls, Mar 25 2001

Keywords

• nonn

Comments

Conjecture: a(n) - 1 is always prime. - Robert Israel, May 04 2025

Examples

			First occurrence of 1 consecutive nonprime gives 4, first occurrence of 2 consecutive nonprimes gives 8 and 9, the first subsequent and disjoint occurrence of 3 consecutive nonprimes gives 14, 15 and 16, etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A060299, A030296.

Programs

Maple

P:= select(isprime, [seq(i,i=3..10^8,2)]):
G:= P[2..-1]-P[1..-2]:
R:= NULL: g:= 1:
for i from 1 to nops(G) do
 gi:= G[i]; ri:= P[i]+1;
 while gi > g do
   R:= R, ri;
   ri:= ri + g;
   gi:= gi - g;
   g:= g+1;
 od;
od:
R; # Robert Israel, May 04 2025

Extensions

Better description and more terms from Larry Reeves (larryr(AT)acm.org), Apr 02 2001

Further terms from Michel ten Voorde Apr 10 2001

Missing a(16)=1070 inserted by Sean A. Irvine, Oct 21 2022