A329795 a(n) = smallest positive k such that scan_diff(k,n) is a square, where scan_diff is defined in the Comments.

2, 1, 2, 3, 1, 2, 3, 4, 5, 3, 1, 2, 3, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 1, 2, 1, 2, 3, 4, 5, 1, 2, 3, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 1, 2, 1, 2, 3, 4, 5, 6

Offset

1,1

Comments

Write i, j in base 10 aligned to right, say

i = bcd...ef

j = .gh...pq

Then scan_diff(i,j) = |b-0| + |c-g| + |d-h| + ... + |e-p| + |f-q|.

Example: scan_diff(12345,909) = 1+2+6+4+4 = 17.

Suggested by the definition of "box" in A329794.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..25000

Example

For n = 1 the smallest k producing a square is 2 (as scan_diff(1,2) = 1);
For n = 2 the smallest k producing a square is 1 (as scan_diff(2,1) = 1);
For n = 3 the smallest k producing a square is 2 (as scan_diff(3,2) = 1);
For n = 5 the smallest k producing a square is 1 (as scan_diff(5,1) = 4);
For n = 16 the smallest k producing a square is 3 (as scan_diff(16,3) = 1+3 = 4).

Prog

(PARI) scan_diff(n, k) = if (n*k, scan_diff(n\10, k\10)+abs((n%10)-(k%10)), n+k)
a(n) = for (k=1, oo, my (t=scan_diff(n, k)); if (t && issquare(t), return (k))) \\ Rémy Sigrist, Dec 08 2019

Crossrefs

Cf. A329794.

Sequence in context: A194029 A194055 A162192 * A329794 A238954 A238967

Adjacent sequences: A329792 A329793 A329794 * A329796 A329797 A329798

Keyword

nonn,base

Author

N. J. A. Sloane, Dec 07 2019

Extensions

More terms from Rémy Sigrist, Dec 08 2019

Status

approved