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A302721
Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the distance from n to the nearest prime(k)-smooth number (where prime(k) denotes the k-th prime number).
0
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0
OFFSET
1,16
FORMULA
a(2^i, k) = 0 for any i >= 0.
a(2*n, k) <= 2*a(n, k).
a(n, k+1) <= a(n, k).
abs(T(n+1, k) - T(n, k)) <= 1.
a(n, A061395(n)) = 0 for any n > 1.
a(n, 1) = A053646(n).
a(n, 2) = A301574(n).
Sum_{k > 0} a(n, k) = A303545(n).
EXAMPLE
Array T(n, k) begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
---+------------------------------------------------------------
1| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3| 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5| 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6| 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7| 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9| 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10| 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11| 3 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12| 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13| 3 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PROG
(PARI) gpf(n) = if (n==1, 1, my (f=factor(n)); f[#f~, 1])
T(n, k) = my (p=prime(k)); for (d=0, oo, if (gpf(n-d) <= p || gpf(n+d) <= p, return (d)))
CROSSREFS
Cf. A053646 (first column), A061395, A301574 (second column), A303545 (row sums).
Sequence in context: A057764 A010108 A033782 * A321740 A098082 A321921
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Apr 29 2018
STATUS
approved