login
A354940
Square array A(n, k) = A354930(n, k)/n, read by falling antidiagonals.
10
1, 2, 3, 3, 5, 4, 4, 7, 7, 5, 5, 9, 13, 9, 3, 7, 11, 16, 13, 6, 7, 8, 13, 19, 17, 8, 13, 4, 9, 17, 25, 21, 11, 19, 5, 3, 11, 19, 31, 25, 13, 25, 8, 9, 5, 13, 23, 37, 29, 16, 31, 11, 11, 7, 11, 16, 25, 43, 37, 23, 37, 15, 17, 10, 31, 3, 17, 27, 49, 41, 26, 43, 19, 19, 14, 41, 4, 13, 19, 29, 61, 49, 31, 49, 22, 25, 16, 51, 6, 25, 7
OFFSET
1,2
COMMENTS
Array is read by descending antidiagonals with (n,k) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), etc.
EXAMPLE
The top left 15x16 corner of the array:
n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-----+---------------------------------------------------------------------
1 | 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25,
2 | 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41,
3 | 4, 7, 13, 16, 19, 25, 31, 37, 43, 49, 61, 64, 67, 73, 79,
4 | 5, 9, 13, 17, 21, 25, 29, 37, 41, 49, 53, 57, 61, 73, 81,
5 | 3, 6, 8, 11, 13, 16, 23, 26, 31, 36, 41, 43, 46, 51, 53,
6 | 7, 13, 19, 25, 31, 37, 43, 49, 61, 67, 73, 79, 97, 103, 109,
7 | 4, 5, 8, 11, 15, 19, 22, 25, 29, 32, 39, 43, 47, 50, 53,
8 | 3, 9, 11, 17, 19, 25, 27, 33, 41, 43, 49, 57, 59, 67, 73,
9 | 5, 7, 10, 14, 16, 19, 23, 25, 28, 32, 37, 41, 43, 46, 50,
10 | 11, 31, 41, 51, 61, 71, 81, 91, 101, 121, 131, 141, 151, 171, 181,
11 | 3, 4, 6, 9, 12, 15, 17, 23, 25, 28, 31, 34, 37, 45, 47,
12 | 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 145, 157, 169, 181, 193,
13 | 7, 8, 9, 11, 14, 20, 22, 23, 27, 33, 37, 40, 46, 47, 48,
14 | 5, 15, 19, 29, 43, 47, 57, 61, 71, 89, 99, 103, 113, 127, 131,
15 | 4, 8, 16, 19, 23, 31, 38, 46, 49, 53, 61, 64, 76, 79, 83,
16 | 7, 11, 13, 17, 23, 27, 29, 33, 43, 49, 59, 61, 65, 71, 75,
PROG
(PARI)
up_to = 105;
A345992(n) = for(m=1, oo, if((m*(m+1))%n==0, return(gcd(n, m))));
memoA354930sq = Map();
A354930sq(n, k) = { my(v=0); if(!mapisdefined(memoA354930sq, [n, k-1], &v), if(1==k, v=0, v = A354930sq(n, k-1))); for(i=1+v, oo, if(A345992(i)==n, mapput(memoA354930sq, [n, k], i); return(i))); };
A354940sq(n, k) = (A354930sq(n, k)/n);
A354940list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A354940sq(col, (a-(col-1))))); (v); };
v354940 = A354940list(up_to);
A354940(n) = v354940[n];
CROSSREFS
Cf. A354932 (column 1).
Rows 1 .. 7 (some of these are conjectural): A000961, A061345 (without its initial 1), A137827, A354934, A354935, A354936, A354937, A354938, A354939.
Sequence in context: A375465 A257004 A126571 * A210874 A244796 A080391
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Jun 15 2022
STATUS
approved