A328464 Square array A(n,k) = A276156((2^(n-1)) * (2k-1)) / A002110(n-1), read by descending antidiagonals.

1, 3, 1, 7, 4, 1, 9, 16, 6, 1, 31, 19, 36, 8, 1, 33, 106, 41, 78, 12, 1, 37, 109, 386, 85, 144, 14, 1, 39, 121, 391, 1002, 155, 222, 18, 1, 211, 124, 421, 1009, 2432, 235, 324, 20, 1, 213, 1156, 426, 1079, 2443, 4200, 341, 438, 24, 1, 217, 1159, 5006, 1086, 2575, 4213, 7430, 457, 668, 30, 1, 219, 1171, 5011, 17018, 2586, 4421, 7447, 12674, 691, 900, 32, 1

Offset

1,2

Comments

Array is read by falling antidiagonals with n (row) and k (column) ranging as: (n,k) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...

Row n contains all such sums of distinct primorials whose least significant summand is A002110(n-1), with each sum divided by that least significant primorial, which is also the largest primorial which divides that sum.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array

Index entries for sequences related to primorial base

Formula

A(n,k) = A276156((2^(n-1)) * (2k-1)) / A002110(n-1).

a(n) = A328461(A135764(n)). [When all sequences are considered as one-dimensional]

Example

Top left 9 X 11 corner of the array:
1: | 1,  3,   7,   9,    31,    33,    37,    39,    211,    213,    217
2: | 1,  4,  16,  19,   106,   109,   121,   124,   1156,   1159,   1171
3: | 1,  6,  36,  41,   386,   391,   421,   426,   5006,   5011,   5041
4: | 1,  8,  78,  85,  1002,  1009,  1079,  1086,  17018,  17025,  17095
5: | 1, 12, 144, 155,  2432,  2443,  2575,  2586,  46190,  46201,  46333
6: | 1, 14, 222, 235,  4200,  4213,  4421,  4434,  96578,  96591,  96799
7: | 1, 18, 324, 341,  7430,  7447,  7753,  7770, 215442, 215459, 215765
8: | 1, 20, 438, 457, 12674, 12693, 13111, 13130, 392864, 392883, 393301
9: | 1, 24, 668, 691, 20678, 20701, 21345, 21368, 765050, 765073, 765717

Prog

(PARI)
up_to = 105;
A002110(n) = prod(i=1, n, prime(i));
A276156(n) = { my(p=2, pr=1, s=0); while(n, if(n%2, s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };
A328464sq(n, k) = (A276156((2^(n-1)) * (k+k-1)) / A002110(n-1));
A328464list(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] = A328464sq(col, (a-(col-1))))); (v); };
v328464 = A328464list(up_to);
A328464(n) = v328464[n];

Crossrefs

Cf. A328463 (transpose).

Cf. A000265, A002110, A007814, A135764, A276154, A276156,

Rows 1 - 5: A328462, A328465, A328466, A328467, A328468.

Column 2: A008864.

Column 3: A023523 (after its initial term).

Column 4: A286624.

Cf. also arrays A276945, A286625.

Sequence in context: A095868 A140962 A013602 * A323956 A086272 A104709

Adjacent sequences: A328461 A328462 A328463 * A328465 A328466 A328467

Keyword

nonn,tabl

Author

Antti Karttunen, Oct 16 2019

Status

approved