A257763 - OEIS

A257763

Zeroless numbers n such that n and n^2 have the same set of decimal digits.

1, 4762, 4832, 12385, 14829, 26394, 34196, 36215, 49827, 68474, 72576, 74528, 79286, 79836, 94583, 94867, 96123, 98376, 123385, 123546, 124235, 124365, 124579, 124589, 125476, 125478, 126969, 129685, 135438, 139256, 139261, 139756, 149382, 152385, 156242

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

{A029793} intersect {A052382}.

EXAMPLE

4762 is in the sequence because it is zeroless and 4762^2 = 22676644 has the same set of decimal digits as 4762: {2,4,6,7}.

MAPLE

a:= proc(n) option remember; local k, s;

for k from 1+`if`(n=1, 0, a(n-1)) do

s:= {convert(k, base, 10)[]};

if not 0 in s and s={convert(k^2, base, 10)[]}

then return k fi

end:

seq(a(n), n=1..10);

MATHEMATICA

sameQ[n_]:=Union[IntegerDigits[n]]==Union[IntegerDigits[n^2]]; Select[Range@156242, And[FreeQ[IntegerDigits[#], 0], sameQ[#]]&] (* Ivan N. Ianakiev, May 08 2015 *)

PROG

(Python)

A257763_list = [n for n in range(1, 10**6) if not '0' in str(n) and set(str(n)) == set(str(n**2))] # Chai Wah Wu, May 31 2015

(PARI) isok(n) = vecmin(d=digits(n)) && Set(d) == Set(digits(n^2)); \\ Michel Marcus, May 31 2015

CROSSREFS

Cf. A029793, A052382, A257760.

Sequence in context: A250467 A183267 A258231 * A260293 A031567 A031747

Adjacent sequences: A257760 A257761 A257762 * A257764 A257765 A257766

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, May 07 2015

STATUS

approved