A391928 Irregular table T(n, k) = (k*A002110(n-1)) mod prime(n), n >= 0, k = 0..prime(n)-1, read by rows, with row 0 = {0} by convention.

0, 0, 1, 0, 2, 1, 0, 1, 2, 3, 4, 0, 2, 4, 6, 1, 3, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 9, 5, 1, 10, 6, 2, 11, 7, 3, 12, 8, 4, 0, 8, 16, 7, 15, 6, 14, 5, 13, 4, 12, 3, 11, 2, 10, 1, 9, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 7, 22, 14, 6, 21, 13, 5, 20, 12, 4, 19, 11, 3, 18, 10, 2, 17, 9, 1, 16, 8

Offset

0,5

Comments

The next row after rows n=1, 3 and 5 with an ascending run of terms 0, 1, 2, 3, ..., is row A341805(4)+1 = 9823713. See Jeppe Stig Nielsen's Feb 20 2021 comment in A079276, and how it affects A391929.

Links

Antti Karttunen, Table of n, a(n) for n = 0..18189; rows 0..88 of the triangle

Index entries for sequences related to primorial numbers.

Formula

T(n, k) = (k*A062347(n-1)) mod prime(n).

Example

n p_n | row
------+-----
0   1 | 0,
1   2 | 0, 1,
2   3 | 0, 2, 1,
3   5 | 0, 1, 2, 3, 4,
4   7 | 0, 2, 4, 6, 1, 3, 5,
5  11 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
6  13 | 0, 9, 5, 1, 10, 6, 2, 11, 7, 3, 12, 8, 4,
7  17 | 0, 8, 16, 7, 15, 6, 14, 5, 13, 4, 12, 3, 11, 2, 10, 1, 9,
8  19 | 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,
9  23 | 0, 15, 7, 22, 14, 6, 21, 13, 5, 20, 12, 4, 19, 11, 3, 18, 10, 2, 17, 9, 1, 16, 8,

Prog

(PARI)
rows_up_to = 35;
A007504(n) = sum(k=1, n, prime(k));
A002110(n) = prod(i=1, n, prime(i));
A391928_tr(n, k) = ((k*A002110(n-1))%prime(n));
A391928_list(rows_up_to) = { my(v = vector(A007504(rows_up_to)), j=0); for(row=1, rows_up_to, for(k=0, prime(row)-1, j++; v[j] = A391928_tr(row, k))); (v); };
v391928 = A391928_list(rows_up_to);
A391928(n) = if(!n, n, v391928[n]);

Crossrefs

Cf. A002110, A007504, A062347 (second column), A079276, A341805, A391929.

Cf. also A060735.

Sequence in context: A179765 A004074 A245615 * A053646 A080776 A376813

Adjacent sequences: A391925 A391926 A391927 * A391929 A391930 A391931

Keyword

nonn,tabf,look

Author

Antti Karttunen, Jan 04 2026

Status

approved