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

1,1

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

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)

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A054037.

Cf. A235717-A235723, A225218.

A036744 is a subsequence.

Sequence in context: A116670 A073643 A235161 * A241792 A112717 A114679

Adjacent sequences: A235721 A235722 A235723 * A235725 A235726 A235727

Keyword

nonn,base

Author

Colin Barker, Jan 15 2014

Status

approved