A253635 Rectangular array read by upwards antidiagonals: a(n,k) = index of largest term <= 10^k in row n of A253572, n >= 1, k >= 0.

1, 1, 4, 1, 7, 7, 1, 9, 20, 10, 1, 10, 34, 40, 14, 1, 10, 46, 86, 67, 17, 1, 10, 55, 141, 175, 101, 20, 1, 10, 62, 192, 338, 313, 142, 24, 1, 10, 67, 242, 522, 694, 507, 190, 27, 1, 10, 72, 287, 733, 1197, 1273, 768, 244, 30

Offset: 1

Author

L. Edson Jeffery, Jan 07 2015

Keywords

• nonn
• tabl

Comments

Or a(n,k) = the number of positive integers less than or equal to 10^k that are divisible by no prime exceeding prime(n).

Examples

			Array begins:
{1,  4,  7,  10,   14,   17,    20,    24,    27,     30, ...}
{1,  7, 20,  40,   67,  101,   142,   190,   244,    306, ...}
{1,  9, 34,  86,  175,  313,   507,   768,  1105,   1530, ...}
{1, 10, 46, 141,  338,  694,  1273,  2155,  3427,   5194, ...}
{1, 10, 55, 192,  522, 1197,  2432,  4520,  7838,  12867, ...}
{1, 10, 62, 242,  733, 1848,  4106,  8289, 15519,  27365, ...}
{1, 10, 67, 287,  945, 2579,  6179, 13389, 26809,  50351, ...}
{1, 10, 72, 331, 1169, 3419,  8751, 20198, 42950,  85411, ...}
{1, 10, 76, 369, 1385, 4298, 11654, 28434, 63768, 133440, ...}
{1, 10, 79, 402, 1581, 5158, 14697, 37627, 88415, 193571, ...}
		

Crossrefs

Cf. A123384, A100752, A106598, A106600, A107352, A106629, A108275, A108276, A108277 (rows 1-9).

Cf. A011557, A066343, A253572, A253573.

Programs

Mathematica

r = 10; y[1] = t = Table[2^j, {j, 0, 39}]; max = 10^13; len = 10^10; prev = 0; For[n = 2, n <= r, n++, next = 0; For[k = 1, k <= 43, k++, If[Prime[n]^k < max, t = Union[t, Prime[n]*t]; s = FirstPosition[t, v_ /; v > len, 0]; t = Take[t, s[[1]] - 1]; If[t[[-1]] > len, t = Delete[t, -1]]; next = Length[t]; If[next == prev, Break, prev = next], Break]]; y[n] = t]; b[i_, j_] := FirstPosition[y[i], v_ /; v > 10^j][[1]]; a253635[n_, j_] := If[IntegerQ[b[n, j]], b[n, j] - 1, 0]; Flatten[Table[a253635[n - j, j], {n, r}, {j, 0, n - 1}]] (* array antidiagonals flattened *)