A284046 Numbers k, not ending in 0, such that the consecutive digits of k^2 differ by 0 or 1.

1, 2, 3, 11, 26, 111, 1111, 11111, 105462, 111111, 460688, 753576, 1111111, 2806538, 3513626, 5858612, 11111111, 23335688, 111111111, 674874474, 8226042716, 2131535935501, 81655720279388

Offset: 1

Author

Giovanni Resta, Mar 19 2017

Keywords

• nonn
• base
• more

Comments

Equivalently, numbers not ending in 0, whose square belong to A032981.

All members k ending in 1 are generators of infinite numbers of the form k*10^e which satisfy the same property. In a sense, here we list only "primitive" terms, not ending in 0.

a(24) > 10^17, if it exists.

Examples

			81655720279388 belongs to this sequence because the consecutive digits of its square, 6667656654345656676777654544, differ by 0 or 1.
		

Crossrefs

Cf. A032981, A048412, A079036.

Programs

Mathematica

Select[Range[10^6], Mod[#, 10] > 0 && Max@ Abs@ Differences@ IntegerDigits[ #^2] <= 1 &]