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

Author

N. J. A. Sloane, Dec 07 2019

Keywords

• nonn
• base

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.

Examples

			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).
		

Links

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

Crossrefs

Cf. A329794.

Programs

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

Extensions

More terms from Rémy Sigrist, Dec 08 2019