# A087646, Wilson vs. Wilson

Don Reble djr at nk.ca
Fri Sep 26 16:25:36 CEST 2003

```> %I A087646
> %S A087646 26,2,5,28
> %N A087646 Starting term of the smallest string of n consecutive
>     power-free numbers.
> %e A087646 We have a(3)=5 because (5,6,7) is the smallest power-free
>    consecutive triple followed by (33,34,35),(122,123,124),...
> %Y A087646 Cf. A001597, A053289.
> %K A087646 hard,more,nonn,new
> %O A087646 1,1
> %A A087646 Lekraj Beedassy (beedassylekraj(AT)hotmail.com), Sep 23 2003

For those who don't get it, A[n] is the first term of the first sequence
of _exactly_ n consecutive non-powers.

The sequence may have gaps: indeed if the conjectural A023057 is
accurate, A087646[A023057[n]-1] is undefined. So one might consider
putting it this way:

%I A087646
%S A087646 26,2,5,28,0,10,97337,17,2188,3126,2198,37,0,50,129,65,226,82,
%T A087646 197,101,0,2026,1001,145,42850,170,485,0,6860,0,7745,257,0,
%U A087646 290,1729,14348908,1332,362,2705,401,0,442,0,9217,0,530,21905
%N A087646 First term of the first sequence of exactly n consecutive non-powers; or zero if there isn't such a sequence.
%e A087646 a(3)=5 because (5,6,7) is the smallest consecutive triple of non-powers, followed by (33,34,35), (122,123,124), ...
%e A087646 The zeroes above are conjectured, and correspond to terms of A023057.
%Y A087646 Cf. A001597, A023057, A053289.
%K A087646 hard,nonn
%O A087646 1,1
%A A087646 Lekraj Beedassy (beedassylekraj(AT)hotmail.com), Sep 23 2003

---

BTW, A023057 and A077287 are the same sequence. (It's good that the
Wilsons agree.)

--
Don Reble       djr at nk.ca

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