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A324351 Square array read by antidiagonals: A(x,y) is the result from writing x and y in primorial base (A049345) and starting from their least significant ends, always choosing a minimal digit from each digit position, and converting back to decimal. 5
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 3, 2, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 3, 4, 3, 0, 1, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 1, 2, 1, 0, 5, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 0, 0, 0, 2, 2, 2, 2, 6, 6, 2, 2, 2, 2, 0, 0, 0, 1, 0, 3, 4, 3, 6, 7, 6, 3, 4, 3, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65702 (the first 362 antidiagonals of the array)

Index entries for sequences related to primorial base

FORMULA

A(x,y) = A276085(A324350(x,y)) = A276085(gcd(A276086(x), A276086(y))).

EXAMPLE

The array A begins:

       0   1   2   3   4   5   6   7   8   9  10  11  12

  x/y  ------------------------------------------------------

   0:  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ...

   1:  0,  1,  0,  1,  0,  1,  0,  1,  0,  1,  0,  1,  0, ...

   2:  0,  0,  2,  2,  2,  2,  0,  0,  2,  2,  2,  2,  0, ...

   3:  0,  1,  2,  3,  2,  3,  0,  1,  2,  3,  2,  3,  0, ...

   4:  0,  0,  2,  2,  4,  4,  0,  0,  2,  2,  4,  4,  0, ...

   5:  0,  1,  2,  3,  4,  5,  0,  1,  2,  3,  4,  5,  0, ...

   6:  0,  0,  0,  0,  0,  0,  6,  6,  6,  6,  6,  6,  6, ...

   7:  0,  1,  0,  1,  0,  1,  6,  7,  6,  7,  6,  7,  6, ...

   8:  0,  0,  2,  2,  2,  2,  6,  6,  8,  8,  8,  8,  6, ...

   9:  0,  1,  2,  3,  2,  3,  6,  7,  8,  9,  8,  9,  6, ...

  10:  0,  0,  2,  2,  4,  4,  6,  6,  8,  8, 10, 10,  6, ...

  11:  0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11,  6, ...

  12:  0,  0,  0,  0,  0,  0,  6,  6,  6,  6,  6,  6, 12, ...

etc.

In primorial base, 5 is written as "21" (as 5 = 2*2 + 1*1) and 10 is written as "120" (as 10 = 1*6 + 2*2 + 0*1). Aligning them digit by digit (from the least significant end), and then always choosing a lesser digit leaves us with digits "020", which is 4 written in primorial base as 2*2 + 0*1 = 4, thus A(5,10) = A(10,5) = 4.

PROG

(PARI)

up_to = 65703; \\ = binomial(362+1, 2)

A002110(n) = prod(i=1, n, prime(i));

A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };

A324351sq(row, col) = A276085(gcd(A276086(row), A276086(col)));

A324351list(up_to) = { my(v = vector(up_to), i=0); for(a=0, oo, for(col=0, a, if(i++ > up_to, return(v)); v[i] = A324351sq(a-col, col))); (v); };

v324351 = A324351list(up_to);

A324351(n) = v324351[1+n]; \\ Antti Karttunen, Feb 25 2019

CROSSREFS

Cf. A001477 (central diagonal), A002110, A049345, A276085, A276086, A324350.

Sequence in context: A275948 A073253 A004198 * A116402 A093323 A106278

Adjacent sequences:  A324348 A324349 A324350 * A324352 A324353 A324354

KEYWORD

nonn,base,tabl

AUTHOR

Antti Karttunen, Feb 25 2019

STATUS

approved

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)