1,2

Next term is 1.343...*10^160. Of the n^n ways of selecting n terms from {a(1),a(2),...,a(n)}, n!*Sum_k{1<=k<=n}(k-1)^k/k!=A076483(n) ways have a product strictly less than a(1)*a(2)*...*a(n) and this is possibly the smallest sequence with that property. If the definition had been: a(n) is the smallest number such that sum of first n terms is greater than n times a(n-1) starting with a(1)=1, then the resulting sequence would have been A003422.

a(n) = 1 + floor[a(n-1)^n / Product_i{0<i<n}a(i)].

a(4)=1+floor[5^4/(1*2*5)]=1+floor[62.5]=63.

Cf. A076483.

Sequence in context: A134590 A012978 A012949 this_sequence A086560 A133004 A066933

Adjacent sequences: A076627 A076628 A076629 this_sequence A076631 A076632 A076633

nonn

Henry Bottomley (se16(AT)btinternet.com), Oct 22 2002