A261213 Odd numbers n such that n^2 = m + (m+1), where both m and m+1 have no repeated digits.

1, 3, 5, 7, 9, 11, 13, 23, 27, 29, 31, 35, 37, 39, 41, 43, 57, 63, 69, 77, 81, 87, 89, 95, 109, 113, 121, 125, 127, 129, 137, 163, 193, 219, 239, 271, 273, 279, 281, 285, 305, 311, 315, 331, 339, 353, 357, 377, 381, 395, 403, 409, 435, 441, 443, 597

Offset: 1

Author

Pieter Post, Aug 12 2015

Keywords

• nonn
• full
• fini
• base

Comments

This sequence is finite and a(146) = 40797 is the last term. 40797^2 = 1664395209 and 1664395209 = 832197604 + 832197605. These last two numbers both have no repeating digits.

Examples

			5 is in the sequence, because 5^2 = 25. 25 = 12 + 13. 12 and 13 both have no repeating digits.
		

Links

• Pieter Post, Table of n, a(n) for n = 1..146

Crossrefs

Cf. A036745, A071519, A156977.

Programs

Mathematica

nr[n_] := 1 == Max@ DigitCount@ n; Select[ Range[1, 10^5, 2], nr[x= Floor[#^2 / 2]] && nr[x + 1] &] (* Giovanni Resta, Aug 12 2015 *)