A137723 - OEIS

%I #8 Oct 07 2024 11:04:39

%S 10,33,20,55,84,114,390,513,182,200,468,2941,774,65522,1832,1261,1130,

%T 1332,1638,524289,1952,4298,4524,69960,5120,16385,2972,4832,5352,

%U 10801,5592

%N 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.

%C A073490(a(n)+k)>0 for 0<=k<n and A073490(a(n)-1)=A073490(a(n)+n)=0.

%C 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, ...

%C a(32) > 10^11. - _Lucas A. Brown_, Oct 07 2024

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A137723.py">Python program</a>.

%e a(5) = 84: #{84, 85, 86, 87, 88} = 5,

%e 84=[7]*[3*2^2], 84+1=19*5, 84+2=43*2, 84+3=29*3, 84+4=11*2^3.

%Y Cf. A073492.

%K nonn,more,hard

%O 1,1

%A _Reinhard Zumkeller_, Feb 09 2008

%E Discovered a(14) and some more terms from _Sean A. Irvine_, Sep 27 2009