A343727 Numbers with all digits odd whose squares have only one odd digit.

1, 3, 5, 7, 9, 15, 17, 51, 53, 79, 91, 93, 151, 155, 157, 533, 535, 775, 779, 793, 917, 1557, 1571, 1575, 5179, 5333, 5335, 7759, 7799, 9317, 9393, 9395, 15557, 15559, 15755, 51595, 53179, 53333, 53335, 77759, 79151, 79175, 93917, 151151, 155135, 155191

Offset

1,2

Comments

Of course, the one odd digit in the square is always the last digit.

The sequence is infinite because it contains the family of numbers 5, 53, 533, 5333, ....... with squares 25, 2809, 284089, 28440889, 2844408889. .... and respectively 535, 5335, 53335, ... with squares 286225, 28462225, 2844622225, 284446222225, ... - Marius A. Burtea, May 21 2021

Links

Table of n, a(n) for n=1..46.

Example

53179 is a term: all its digits are odd, and 53179^2 = 2828006041 has only one odd digit.
15113133375599 is a term: all its digits are odd, and 15113133375599^2 = 228406800428644424408608801 has only one odd digit.

Mathematica

Select[Range[160000], AllTrue[IntegerDigits[#], OddQ] && AllTrue[Most @ IntegerDigits[#^2], EvenQ] &] (* Amiram Eldar, May 20 2021 *)

Prog

(Python)
def ok(n):
  r, s = str(n), str(n*n)
  return all(d in "13579" for d in r) and all(d in "02468" for d in s[:-1])
print(list(filter(ok, range(1, 155192, 2)))) # Michael S. Branicky, May 20 2021
(Python)
from itertools import product
A343727_list = [n for n in (int(''.join(d)) for l in range(1, 6) for d in product('13579', repeat=l)) if set(str(n**2)[:-1]) <= set('02468')] # Chai Wah Wu, May 21 2021
(Magma) [n:n in [1..160000 by 2]|Set(Intseq(n)) subset {1, 3, 5, 7, 9} and Set(Intseq(n*n div 10)) subset {0, 2, 4, 6, 8}]; // Marius A. Burtea, May 21 2021

Crossrefs

Cf. A014261, A030098, A343726, A343728.

Sequence in context: A076188 A265852 A335132 * A340559 A073674 A084722

Adjacent sequences: A343724 A343725 A343726 * A343728 A343729 A343730

Keyword

nonn,base

Author

Jon E. Schoenfield, May 20 2021

Status

approved