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A360407
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Irregular table T(n, k), n >= 0, k = 0..A002110(n)-1, read by rows; for any k with primorial base expansion (d_n, ..., d_1), T(n, k) is the least number t such that t mod prime(u) = d_u for u = 1..n (where prime(u) denotes the u-th prime number).
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1
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0, 0, 1, 0, 3, 4, 1, 2, 5, 0, 15, 10, 25, 20, 5, 6, 21, 16, 1, 26, 11, 12, 27, 22, 7, 2, 17, 18, 3, 28, 13, 8, 23, 24, 9, 4, 19, 14, 29, 0, 105, 70, 175, 140, 35, 126, 21, 196, 91, 56, 161, 42, 147, 112, 7, 182, 77, 168, 63, 28, 133, 98, 203, 84, 189, 154, 49
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OFFSET
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0,5
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COMMENTS
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When computing T(n, k), we pad the primorial base expansion of k with leading zeros so as to have n digits.
The Chinese remainder theorem ensures that this sequence is well defined and provides a way to compute it.
The n-th row is a permutation of 0..A002110(n)-1.
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LINKS
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FORMULA
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T(n, 0) = 0.
T(n, 1) = A070826(n) for any n > 0.
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EXAMPLE
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Table T(n, k) begins:
0;
0, 1;
0, 3, 4, 1, 2, 5;
0, 15, 10, 25, 20, 5, 6, 21, 16, 1, 26, 11, 12, 27, 22,
7, 2, 17, 18, 3, 28, 13, 8, 23, 24, 9, 4, 19, 14, 29;
...
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PROG
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(PARI) T(n, k) = { my (t=Mod(0, 1)); if (n, forprime (p=2, prime(n), t=chinese(t, Mod(k, p)); k\=p)); lift(t) }
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CROSSREFS
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See A343404 for a similar sequence.
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KEYWORD
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nonn,base,tabf
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AUTHOR
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STATUS
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approved
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