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 A273619 Table read by antidiagonals (n>1, k>0): A(n,k) = leading digit of k in base n. 1
 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 3, 4, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 1, 1, 1, 2, 3, 4, 5, 6, 1, 1, 1, 2, 1, 1, 1, 2, 3, 4, 5, 6, 7, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,5 COMMENTS This is a generalization of A000030. The first occurrence of a number k in the sequence is given by A(k+1,k). LINKS Robert Israel, Table of n, a(n) for n = 2..10012 (first 142 antidiagonals, flattened) FORMULA From Robert Israel, May 31 2016: (Start) A(n,k) = floor(k/n^floor(log_n(k))). A(n,k) = k if n > k. A(n,k) = A(n, floor(k/n)) otherwise. G.f. of row n, G_n(x), satisfies G_n(x) = (1-x^n)/(1-x)^2 - (1+(n-1)*x^n)/(1-x) + (1-x^n)*G_n(x^n)/(1-x). (End) EXAMPLE First few rows of the array are: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1... 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2... 1, 2, 3, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1... 1, 2, 3, 4, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3... 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3... 1, 2, 3, 4, 5, 6, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2... 1, 2, 3, 4, 5, 6, 7, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2... Note that the initial row is row 2. A(3,3) corresponds to row n=3 and column k=3, and k=3 is written as 10 in base n=3, and the leading digit of 10 is 1, so A(3,3)=1. A(12,11) corresponds to row n=12 and column k=11, and 11 is written as B in base 12, and the leading and only digit of B is B which is number 11 in decimal, so A(12,11)=11. MAPLE A:= (n, k) -> floor(k/n^floor(log[n](k))): seq(seq(A(n-k, k), k=1..n-2), n=2..20); # Robert Israel, May 31 2016 MATHEMATICA a[n_, k_] := First[IntegerDigits[k, n]]; PROG (PARI) T(n, k) = digits(k, n)[1]; tabl(10, 10, n, k, n++; T(n, k)); \\ Michel Marcus, Jun 12 2016 CROSSREFS Cf. A000030 (row 10), A122586 (row 3), A122587 (row 4). Cf. A051777, A051778 (may be interpreted as arrays of last digits of k in base n). Sequence in context: A073204 A248641 A282934 * A034003 A168508 A177994 Adjacent sequences:  A273616 A273617 A273618 * A273620 A273621 A273622 KEYWORD tabl,base,easy,nonn AUTHOR Andrey Zabolotskiy, May 30 2016 STATUS approved

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)