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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 LINKS 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 * A098082 A321921 A236419 Adjacent sequences:  A302718 A302719 A302720 * A302722 A302723 A302724 KEYWORD nonn,tabl AUTHOR Rémy Sigrist, Apr 29 2018 STATUS approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)