[seqfan] Re: Smallest hitters

[Maximilian Hasler]

> Take 137, for instance and start a sequence S
> where the differences "d" between two consecutive
> terms of S spell, digit by digit, the sequence S
> itself:
>
> S = 137 138 141 148 149 152 160 161 165 166 ...
> d =    1   3   7   1   3   8   1   4   1
>
> We see that 137 "hits" 166 (for instance) -- but
> is 137 the smallest integer hitting 166? No, it
> is 1 (as one will see following the above link).
>
> What is the sequence of the "smallest hitters"
> (SH) of the natural numbers?
>
> I guess it starts:
>
> n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
> SH = 1 1 3 1 5 3 7 1 9  5  5  3  3  5  3  1  1 ...

I confirm these values and get

vector(150,n,SH(n))
 = [1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 3, 5, 3, 1, 1, 5, 3, 3, 11, 5,
1, 1, 3, 3, 5, 5, 19, 13, 1, 3, 1, 5, 7, 1, 7, 1, 7, 5, 5, 1, 13, 3,
1, 1, 11, 9, 1, 5, 3, 1, 3, 11, 1, 9, 20, 13, 3, 7, 1, 3, 5, 1, 5, 9,
3, 5, 9, 3, 11, 1, 7, 3, 11, 1, 5, 1, 5, 3, 11, 1, 7, 3, 11, 20, 1, 3,
15, 5, 1, 3, 5, 19, 11, 3, 1, 24, 11, 5, 1, 3, 24, 5, 9, 13, 3, 3, 5,
1, 9, 13, 3, 15, 1, 3, 1, 19, 33, 11, 3, 1, 24, 19, 9, 13, 1, 17, 27,
3, 9, 5, 1, 1, 31, 3, 9, 3, 7, 1, 5, 7, 9, 1, 15, 11, 5, 3, 7, 13]

(PARI)
SH(n)={ for(k=1,n, my(seed=k,d=digits(seed));
while(seed<n,seed+=d[1];d=vecextract(concat(d,digits(seed)),"^1"));seed==n&return(k))}

I proposed this as https://oeis.org/draft/A211206

Maximilian


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