A030474 -id:A030474 - cp's OEIS frontend

A030476 Squares with property that all even digits occur together and all odd digits occur together.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 144, 196, 225, 289, 324, 400, 441, 484, 576, 625, 784, 841, 900, 1024, 1156, 1444, 1600, 1764, 1936, 2025, 2209, 2401, 2601, 2809, 3136, 3364, 3600, 3844, 4225, 4489, 4624, 5184, 5776, 6084, 6241, 6400

Offset: 1

Patrick De Geest

Among first 22083 terms (up to 10^14), there are 19202 even and 2881 odd terms. Also note that in odd terms, the only odd digit is the last one. - Zak Seidov, Apr 17 2016
From Robert Israel, Apr 18 2016: (Start)
For any k>=1, (10^k-2)^2 is a member of the sequence with the first k-1 digits odd and the last k+1 even, while (2*10^k+2)^2 = 4*10^(2*k)+8*10^k+4 is a member with all digits even, and (2*10^k+1)^2 is an odd member.
If x is an even member, then so is 100*x. (End)

			a(21055) = 9427771^2 = 88882866028441, - _Zak Seidov_, Apr 18 2016
a(21056) = 9427980^2 = 88886806880400. - _Robert Israel_, Apr 18 2016

Zak Seidov, Table of n, a(n) for n = 1..22083

Setwise difference A000290 \ A030474.

Cf. A030477.

filter:= proc(n) local L,evens,odds;
L:= convert(n,base,10) mod 2;
evens:= select(t -> L[t]::even, [$1..nops(L)]);
odds:= select(t -> L[t]::odd, [$1..nops(L)]);
(evens = []) or (odds = []) or (evens[1]>odds[-1]) or (odds[1]>evens[-1])
end proc:
select(filter, [seq(i^2,i=0..100)]); # Robert Israel, Apr 18 2016

Select[Range[0, 80]^2, Function[k, Or[Flatten@ # == k, Flatten@ Reverse@ # == k] &@ GatherBy[k, EvenQ]]@ IntegerDigits@ # &] (* Michael De Vlieger, Apr 17 2016 *)

a(n) = A030477(n)^2. - Andrew Howroyd, Aug 11 2024

Offset corrected by Andrew Howroyd, Aug 11 2024

A030479 Cubes with property that all even digits occur together and all odd digits occur together.

Original entry on oeis.org

0, 1, 8, 27, 64, 512, 1000, 1331, 1728, 2197, 3375, 4913, 6859, 8000, 10648, 13824, 17576, 29791, 35937, 39304, 42875, 59319, 64000, 74088, 97336, 140608, 157464, 195112, 205379, 357911, 373248, 512000, 551368, 753571, 778688

Offset: 1

Patrick De Geest

Setwise difference A000578 \ A030474.

Cf. A030478.

a(n) = A030478(n)^3. - Andrew Howroyd, Aug 11 2024

Offset corrected by Andrew Howroyd, Aug 11 2024

cp's OEIS Frontend

A030476 Squares with property that all even digits occur together and all odd digits occur together.

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