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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 (list; table; graph; refs; listen; history; text; internal format)
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.
LINKS
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: A268087 A257004 A126571 * A210874 A244796 A080391
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Jun 15 2022
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)