The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A329041 Square array read by antidiagonals: A(n, k) = A327936(A276086(n) * A276086(k)). 3
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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), ... 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. LINKS FORMULA A(n, k) = A327936(A276086(n) * A276086(k)). For all n, A(A328841(n), A328842(n)) = 1 and A(A328770(n), A328770(n)) = 1. EXAMPLE The top left corner of the array:         0  1  2  3  4  5  6  7  8  9 10 11 12       +--------------------------------------    0: | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...    1: | 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...    2: | 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 1, ...    3: | 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, ...    4: | 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, ...    5: | 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, ...    6: | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...    7: | 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...    8: | 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 1, ...    9: | 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, ...   10: | 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, ...   11: | 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, ...   12: | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... ... 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. PROG (PARI) up_to = 105; A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); }; A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); }; A329041sq(row, col) = A327936(A276086(row)*A276086(col)); 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); }; v329041 = A329041list(up_to); A329041(n) = v329041[1+n]; CROSSREFS Cf. A049345, A276086, A327936. Cf. also A317836, A324351, A328770, A328841, A328842. Sequence in context: A178085 A078572 A122750 * A238744 A030421 A085021 Adjacent sequences:  A329038 A329039 A329040 * A329042 A329043 A329044 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Nov 03 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 03:38 EDT 2022. Contains 356029 sequences. (Running on oeis4.)