cp's OEIS Frontend

A329041 Square array read by antidiagonals: A(n, k) = A327936(A276086(n) * A276086(k)).

%I A329041 #14 Nov 07 2019 14:39:27
%S A329041 1,1,1,1,2,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,2,3,2,3,2,1,1,1,3,3,3,3,
%T A329041 1,1,1,2,1,6,3,6,1,2,1,1,1,1,1,3,3,1,1,1,1,1,2,1,2,1,6,1,2,1,2,1,1,1,
%U A329041 1,1,1,1,1,1,1,1,1,1,1,2,3,2,3,2,1,2,3,2,3,2,1,1,1,3,3,3,3,1,1,3,3,3,3,1,1
%N A329041 Square array read by antidiagonals: A(n, k) = A327936(A276086(n) * A276086(k)).
%C A329041 Array A(n, k) is symmetric, and is read as (n,k) = (0, 0), (1, 0), (0, 1), (2, 0), (1, 1), (0, 2), (3, 0), (2, 1), (1, 2), (0, 3), ...
%C A329041 If A(n, k) is 1, it tells that adding of n and k do not generate any carries, when done in primorial base (A049345). If A(n, k) is larger than one, then its prime factors indicate in which specific moduli (digit positions) the sum was larger than allowed for that position.
%H A329041 Antti Karttunen, <a href="/A329041/b329041.txt">Table of n, a(n) for n = 0..10439; the first 144 antidiagonals of the array</a>
%H A329041 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A329041 A(n, k) = A327936(A276086(n) * A276086(k)).
%F A329041 For all n, A(A328841(n), A328842(n)) = 1 and A(A328770(n), A328770(n)) = 1.
%e A329041 The top left corner of the array:
%e A329041         0  1  2  3  4  5  6  7  8  9 10 11 12
%e A329041       +--------------------------------------
%e A329041    0: | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A329041    1: | 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
%e A329041    2: | 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 1, ...
%e A329041    3: | 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, ...
%e A329041    4: | 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, ...
%e A329041    5: | 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, ...
%e A329041    6: | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A329041    7: | 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
%e A329041    8: | 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 1, ...
%e A329041    9: | 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, ...
%e A329041   10: | 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, ...
%e A329041   11: | 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, ...
%e A329041   12: | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A329041 ...
%e A329041 A(11,25) = A(25,11) = 10 because 11 is written in primorial base representation (A049345) as "121" and 25 as "401", and when these are added together digit by digit, we see that the maximal allowed digits "421" for the rightmost three positions are exceeded in positions 1 and 3, with the 1st and 3rd primes 2 and 5 as their moduli, thus A(11,25) = 2*5 = 10.
%o A329041 (PARI)
%o A329041 up_to = 105;
%o A329041 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329041 A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]>=f[k,1])); factorback(f); };
%o A329041 A329041sq(row,col) = A327936(A276086(row)*A276086(col));
%o A329041 A329041list(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] = A329041sq(a-col,col))); (v); };
%o A329041 v329041 = A329041list(up_to);
%o A329041 A329041(n) = v329041[1+n];
%Y A329041 Cf. A049345, A276086, A327936.
%Y A329041 Cf. also A317836, A324351, A328770, A328841, A328842.
%K A329041 nonn,tabl
%O A329041 0,5
%A A329041 _Antti Karttunen_, Nov 03 2019