[seqfan] Re: Erased copies

[Hans Havermann]

EA: "A sequence I would like to see is the one dealing with the function F = (n+1)*a(n) that would generate, for the smallest a(1), more than 100 terms." ... "A friend of mine thinks that no integer < 10000000 generates any 100-term sequence, according to a program he wrote: the longest sequence would have 78 terms and the smallest generating-term would be 19128."

By restricting ourselves to the (fewer than nine million) terms of A010784, it appears that 78 is indeed the longest sequence thus generated. Of that length, I found 1746 solutions that all share the identical 20th term of 180 (and therefore also share terms 21 to 78). The solution with the smallest starting number is 24603.

Using F = prime(n)*a(n) instead of F = (n+1)*a(n) allows sequences with as many as 362 terms. Of that length, I found 785 solutions that all share the identical 45th term of 3. The solution with the smallest starting number is 102735.