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%I #27 May 02 2018 09:21:56
%S 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,
%T 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,
%U 0,0,0,0,0,0,0,0,0,0,3,0,1,0,0,0,0,0,0
%N 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).
%H <a href="/index/Di#distance_to_the_nearest">Index entries for sequences related to distance to nearest element of some set</a>
%F a(2^i, k) = 0 for any i >= 0.
%F a(2*n, k) <= 2*a(n, k).
%F a(n, k+1) <= a(n, k).
%F abs(T(n+1, k) - T(n, k)) <= 1.
%F a(n, A061395(n)) = 0 for any n > 1.
%F a(n, 1) = A053646(n).
%F a(n, 2) = A301574(n).
%F Sum_{k > 0} a(n, k) = A303545(n).
%e Array T(n, k) begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
%e ---+------------------------------------------------------------
%e 1| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 2| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 3| 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 4| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 5| 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 6| 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 7| 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 8| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 9| 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 10| 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 11| 3 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 12| 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 13| 3 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%o (PARI) gpf(n) = if (n==1, 1, my (f=factor(n)); f[#f~, 1])
%o T(n,k) = my (p=prime(k)); for (d=0, oo, if (gpf(n-d) <= p || gpf(n+d) <= p, return (d)))
%Y Cf. A053646 (first column), A061395, A301574 (second column), A303545 (row sums).
%K nonn,tabl
%O 1,16
%A _Rémy Sigrist_, Apr 29 2018
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