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A356300
Square array read by antidiagonals. A(n,k) is the nearest common ancestor of n and k in the binary tree depicted in A253563.
5
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 4, 3, 4, 7, 4, 3, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1
OFFSET
1,5
COMMENTS
Array is symmetric and is read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ... .
Also the nearest common ancestor of n and k in the tree depicted in A253565 (the mirror image of the A253563-tree).
EXAMPLE
The top left 21x21 corner of the array:
n/k | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
-----+----------------------------------------------------------------------------
1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2 | 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
3 | 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3,
4 | 1, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,
5 | 1, 2, 3, 2, 5, 2, 5, 2, 3, 2, 5, 2, 5, 2, 3, 2, 5, 2, 5, 2, 3,
6 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2,
7 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 7, 2, 7, 2, 3, 2, 7, 2, 7, 2, 3,
8 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 8, 2, 4, 2, 8, 2, 4, 2, 8, 2,
9 | 1, 2, 3, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 9,
10 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 10, 2, 4, 2, 6, 2, 4, 2,
11 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3,
12 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 12, 2, 4, 2, 8, 2, 4, 2, 12, 2,
13 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 13, 2, 13, 2, 3,
14 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 14, 2, 4, 2, 6, 2, 4, 2,
15 | 1, 2, 3, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 15, 2, 3, 2, 3, 2, 15,
16 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 8, 2, 4, 2, 16, 2, 4, 2, 8, 2,
17 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 17, 2, 3,
18 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 18, 2, 4, 2,
19 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3,
20 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 12, 2, 4, 2, 8, 2, 4, 2, 20, 2,
21 | 1, 2, 3, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 15, 2, 3, 2, 3, 2, 21,
.
A(3,6) = A(6,3) = 2 because the nearest common ancestor of 3 and 6 in the tree described in A253563 (and in A253565) is 2.
A(4,6) = A(6,4) = 4 because 6 occurs as a descendant of 4 in A253563-tree, thus their nearest common ancestor is 4 itself.
PROG
(PARI)
up_to = 105;
A253553(n) = if(n<=2, 1, my(f=factor(n), k=#f~); if(f[k, 2]>1, f[k, 2]--, f[k, 1] = precprime(f[k, 1]-1)); factorback(f));
A356300sq(x, y) = if(1==x||1==y, 1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista, k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec, h))>0, return(stemvec[i])); h = A253553(h)));
A356300list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A356300sq(col, (a-(col-1))))); (v); };
v356300 = A356300list(up_to);
A356300(n) = v356300[n];
CROSSREFS
Cf. also A348041.
Sequence in context: A230596 A307079 A330190 * A348041 A003983 A087062
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Aug 03 2022
STATUS
approved