A235724 Squares which have one or more occurrences of exactly nine different digits.

102495376, 102576384, 102738496, 104325796, 105637284, 139854276, 152843769, 157326849, 158306724, 158407396, 172843609, 176039824, 176305284, 178035649, 180472356, 183467025, 187635204, 198753604, 208571364, 215384976, 217356049, 218034756, 235714609

Offset: 1

Author

Colin Barker, Jan 15 2014

Keywords

• nonn
• base

Comments

The first term having a repeated digit is 1005397264.

The smallest penholodigital square is a(6) = A036744(1) = 139854276 and the largest one is a(83) = A036744(30) = 923187456 (see Penguin references). - Bernard Schott, Feb 07 2022

Examples

			102495376 is in the sequence because 102495376 = 10124^2 and 102495376 contains exactly nine different digits: 0, 1, 2, 3, 4, 5, 6, 7 and 9.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised Edition), Penguin Books, 1997, entry 139854276, page 184 and entry 923187456, page 186.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Colin Barker)

Crossrefs

Cf. A054037.

Cf. A235717-A235723, A225218.

A036744 is a subsequence.

Programs

PARI

s=[]; for(n=1, 100000, if(#vecsort(eval(Vec(Str(n^2))),,8)==9, s=concat(s, n^2))); s

Python

from itertools import count, islice
def agen(): yield from (r*r for r in count(10**4) if len(set(str(r*r)))==9)
print(list(islice(agen(), 23))) # Michael S. Branicky, May 24 2022

Formula

a(n) = A054037(n)^2.