A036745 -id:A036745 - cp's OEIS frontend

A383691 Square numbers with distinct digits from 1-9 that have an initial string of two or more digits forming a square number.

169, 256, 361, 3249, 16384, 18496, 36481, 81796, 237169, 729316, 2537649, 3481956, 5184729, 36517849, 81432576, 254817369, 361874529, 529874361

Offset: 1

Hilarie Orman, May 05 2025

The sequence is based on correspondence with Donald S. McDonald. He originated the idea and computed the complete list of terms.

The last two numbers in the sequence are perfect squares with square roots that are digit permutations of each other: 361874529 = 19023*19023 and 529874361 = 23019*23019.

			169 is a term, because 169 and 16 are both squares, and each digit of 169 is unique.
18496 is a term, because 18496 and 1849 are both squares, and each digit of 18496 is unique.

Cf. A036744, A036745, A352329.

dd=Select[Range[11,25000]^2,IntegerLength[#]==CountDistinct[IntegerDigits[#]]&&ContainsNone[IntegerDigits[#],{0}]&];f[n_]:=AnyTrue[Table[FromDigits[Take[IntegerDigits[n],i]],{i,2,IntegerLength[n]-1}]^(1/2),IntegerQ];Select[dd,f[#]&] (* James C. McMahon, May 07 2025 *)

cp's OEIS Frontend

A383691 Square numbers with distinct digits from 1-9 that have an initial string of two or more digits forming a square number.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica