A030152 Squares in which parity of digits alternates.

0, 1, 4, 9, 16, 25, 36, 49, 81, 121, 169, 256, 361, 529, 676, 729, 961, 1296, 4761, 5476, 6561, 7056, 9216, 12321, 12769, 14161, 16129, 18769, 32761, 34969, 41616, 56169, 69696, 72361, 74529, 76729, 78961, 87616, 96721, 147456, 163216, 181476, 212521

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Examples

			1296 is a term as 1, 2, 9 and 6 have odd and even parity alternately.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)

Crossrefs

Cf. A030142, A030143, A030144, A030152, A030153, A030154, A030159.

Intersection of A000290 and A030141.

Programs

Haskell

a030152 n = a030152_list !! (n-1)
a030152_list = filter ((== 1) . a228710) a000290_list
-- Reinhard Zumkeller, Aug 31 2013

Maple

i := 0:for a from 1 to 1000 do b := a^2:g := ceil(log(b+1)/log(10)):iss := true:for j from 1 to g-1 do if((b mod 2)=1) then if((floor(b/10^j) mod 2)=((-1)^(j+1)+1)/2) then iss := false:end if:else if((floor(b/10^j) mod 2)=((-1)^j+1)/2) then iss := false:end if:end if:end do: if(iss=true) then i := i+1:c[i] := b:end if:end do:q := seq(c[k],k=1..i-1); # Sascha Kurz, Mar 23 2002

Mathematica

altQ[n_] := n < 10 || Union[Total /@ Partition[ Mod[ IntegerDigits@n, 2], 2, 1]] == {1}; Select[ Range[0, 500]^2, altQ[#] &] (* Giovanni Resta, Aug 16 2018 *)

Formula

A010052(a(n)) * A228710(a(n)) = 1. - Reinhard Zumkeller, Aug 31 2013

Extensions

Edited by N. J. A. Sloane, Aug 31 2009 at the suggestion of R. J. Mathar

Offset corrected by Reinhard Zumkeller, Aug 31 2013