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A361088
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Irregular table, read by rows, where row n holds the tau signature of n, i.e., the shortest sequence (tau(n+k), 0 <= k <= m) that uniquely identifies n; tau = A000005.
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0
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1, 2, 2, 2, 3, 3, 2, 2, 4, 2, 4, 2, 4, 2, 4, 3, 4, 3, 3, 4, 2, 4, 2, 6, 2, 6, 2, 4, 6, 2, 4, 2, 4, 4, 5, 4, 4, 5, 4, 5, 5, 2, 2, 6, 2, 6, 6, 2, 6, 2, 6, 4, 4, 2, 6, 4, 4, 2, 8, 4, 4, 2, 8, 4, 2, 8, 2, 8, 3, 8, 3, 3, 4, 4, 6, 2, 4, 4, 6, 2, 8, 4, 6, 2, 8, 2, 6, 2, 8, 2, 6, 2, 8
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OFFSET
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1,2
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COMMENTS
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Row lengths are given by A309981(n) + 1; see there (and the OEIS wiki page) for examples.
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LINKS
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EXAMPLE
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The first 20 rows read as follows:
n | row n: tau-signature of n
---+--------------------------
1 | [1]
2 | [2, 2]
3 | [2, 3]
4 | [3, 2]
5 | [2, 4, 2]
6 | [4, 2, 4]
7 | [2, 4, 3]
8 | [4, 3]
9 | [3, 4, 2]
10 | [4, 2, 6]
11 | [2, 6, 2, 4]
12 | [6, 2, 4]
13 | [2, 4, 4, 5]
14 | [4, 4, 5]
15 | [4, 5]
16 | [5, 2]
17 | [2, 6, 2, 6]
18 | [6, 2, 6]
19 | [2, 6, 4, 4, 2]
20 | [6, 4, 4, 2, 8]
See the wiki page for proofs.
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PROG
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(PARI) signatures=Map(); LIMIT=10^5 /* This search limit should (possibly dynamically, or by hand) be increased as n grows beyond 100. As of today, the value for n=49 is not yet proven. */
A361088_row(n, s=0)={if(!s, s=iferr(mapget(signatures, n), E, []); #s|| for(L=1, oo, s=concat(s, numdiv(n+L-1)); A361088_row(n, s)|| [mapput(signatures, n, [s, LIMIT]); return(s)]); s[2]>=LIMIT&& return(s[1]); s=s[1]; while(A361088_row(n, s), s=concat(s, numdiv(n+#r))); mapput(signatures, n, [s, LIMIT]); return(s)); my(r=iferr(mapget(signatures, s), E, [])); if(!r, r=[n, n], r[2]<n, r=[r[1], n, n]; mapput(signatures, s, r); return(n), #r>2, return(r[#r-1]), r[#r]>=LIMIT, return); for(j=max(r[2], n)+1, LIMIT, for(k=1, #s, numdiv(j+k-1)!=s[k]&& next(2)); mapput(signatures, s, [n, j, j]); return(j)); mapput(signatures, s, [n, LIMIT])
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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