A360407 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).

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

Offset

0,5

Comments

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..2558

Wikipedia, Chinese remainder theorem

Index entries for sequences related to primorial base

Formula

T(n, 0) = 0.

T(n, 1) = A070826(n) for any n > 0.

T(n, A002110(n) - 1) = A057588(n) for any n > 0.

T(n, k) + T(n, A002110(n) - 1 - k) = A002110(n) - 1.

Example

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;
    ...

Prog

(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) }

Crossrefs

See A343404 for a similar sequence.

Cf. A002110, A057588, A070826.

Sequence in context: A106650 A076942 A205127 * A343613 A333454 A021971

Adjacent sequences: A360404 A360405 A360406 * A360408 A360409 A360410

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Feb 06 2023

Status

approved