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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

Table of n, a(n) for n=1..87.

Index entries for sequences related to distance to nearest element of some set

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.)