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A253635
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Rectangular array read by upwards antidiagonals: a(n,k) = index of largest term <= 10^k in row n of A253572, n >= 1, k >= 0.
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10
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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
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OFFSET
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1,3
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=1..55.
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EXAMPLE
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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, ...}
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A123384, A100752, A106598, A106600, A107352, A106629, A108275, A108276, A108277 (rows 1-9).
Cf. A011557, A066343, A253572, A253573.
Sequence in context: A156558 A082455 A140657 * A078975 A050411 A010643
Adjacent sequences: A253632 A253633 A253634 * A253636 A253637 A253638
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KEYWORD
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nonn,tabl
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AUTHOR
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L. Edson Jeffery, Jan 07 2015
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STATUS
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approved
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