A356953 - OEIS

A356953

Least nonzero starting number in the first run of exactly n consecutive numbers having the same number of prime factors counted with multiplicity, or -1 if no such number exists.

%I #63 Sep 17 2022 14:14:19

%S 1,2,33,1083,602,2522,211673,6612470,3405122,49799889,202536181,

%T 3195380868,5208143601,85843948321,97524222465

%N Least nonzero starting number in the first run of exactly n consecutive numbers having the same number of prime factors counted with multiplicity, or -1 if no such number exists.

%C In the definition, "exactly" means the run is not part of a longer run.

%e 2 and 3 are 2 consecutive numbers and have the same number of prime factors, and 2 is the smallest such number, hence a(2) = 2.

%o (PARI) card(m)=my(c=0,k=bigomega(m));if(bigomega(m-1)!=k,while(bigomega(m)==k,c++;m++));c

%o a(n)=if(n==1,return(1));for(m=2,+oo,if(card(m)==n,return(m)))

%Y Cf. A001222, A077657, A356855.

%Y Cf. A045920, A115186, A113752, A356893.

%K nonn,more

%O 1,2

%A _Jean-Marc Rebert_, Sep 06 2022