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A030476 Squares with property that all even digits occur together and all odd digits occur together. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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)

LINKS

Zak Seidov, Table of n, a(n) for n = 0..22082

EXAMPLE

a(21054)=9427771^2=88882866028441, - Zak Seidov, Apr 18 2016

a(21055)=9427980^2=88886806880400. - Robert Israel, Apr 18 2016

MAPLE

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A325148 A325149 A326707 * A077355 A077487 A179334

Adjacent sequences:  A030473 A030474 A030475 * A030477 A030478 A030479

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified July 12 11:25 EDT 2020. Contains 335658 sequences. (Running on oeis4.)