A137723 First occurrence of a set of n consecutive numbers having at least one prime gap in their factorization: a(n) = smallest number of this set.

10, 33, 20, 55, 84, 114, 390, 513, 182, 200, 468, 2941, 774, 65522, 1832, 1261, 1130, 1332, 1638, 524289, 1952, 4298, 4524, 69960, 5120, 16385, 2972, 4832, 5352, 10801, 5592

Offset: 1

Author

Reinhard Zumkeller, Feb 09 2008

Keywords

• nonn
• more
• hard

Comments

A073490(a(n)+k)>0 for 0<=kA073490(a(n)-1)=A073490(a(n)+n)=0.

Continuation after the missing a(14): 1832, 1261, 1130, 1332, 1638, missing, 1952,4298, 4524, missing, 5120, 16385, 2972, 4832, 5352, 10801, 5592, missing, 8468, missing, 9552, missing, 39462, missing, 20810, missing, 38502, missing, 15684, ...

a(32) > 10^11. - Lucas A. Brown, Oct 07 2024

Examples

			a(5) = 84: #{84, 85, 86, 87, 88} = 5,
84=[7]*[3*2^2], 84+1=19*5, 84+2=43*2, 84+3=29*3, 84+4=11*2^3.
		

Links

• Lucas A. Brown, Python program.

Crossrefs

Cf. A073492.

Extensions

Discovered a(14) and some more terms from Sean A. Irvine, Sep 27 2009