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

1,1

Comments

A073490(a(n)+k)>0 for 0<=k<n and A073490(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

Links

Table of n, a(n) for n=1..31.

Lucas A. Brown, Python program.

Example

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.

Crossrefs

Cf. A073492.

Sequence in context: A265374 A231032 A232009 * A256352 A255533 A067878

Adjacent sequences: A137720 A137721 A137722 * A137724 A137725 A137726

Keyword

nonn,more,hard

Author

Reinhard Zumkeller, Feb 09 2008

Extensions

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

Status

approved