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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Intersection of A000290 and A030141.

Sequence in context: A369567 A340674 A068879 * A030288 A030154 A122541

Adjacent sequences: A030149 A030150 A030151 * A030153 A030154 A030155

Keyword

nonn,base

Author

Patrick De Geest

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

Status

approved