A030153 -id:A030153 - cp's OEIS frontend

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

Patrick De Geest

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

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

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

Intersection of A000290 and A030141.

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

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

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 *)

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

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

Offset corrected by Reinhard Zumkeller, Aug 31 2013

A030151 Numbers k such that in k^2 the parity of digits alternates.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 23, 26, 27, 31, 36, 69, 74, 81, 84, 96, 111, 113, 119, 127, 137, 181, 187, 204, 237, 264, 269, 273, 277, 281, 296, 311, 384, 404, 426, 461, 463, 539, 574, 584, 606, 661, 673, 677, 689, 726, 736, 764, 819

Offset: 1

Patrick De Geest

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A030152, A030153, A030154, A030159.

upto=2000;tfs=Flatten[Table[{True,False},{Ceiling[IntegerLength[ upto]]}]]; altparQ[n_]:= Module[{n2=n^2},MemberQ[Partition[ tfs,IntegerLength[n2],1], EvenQ/@IntegerDigits[n2]]]; Join[{0},Select[Range[upto],altparQ]] (* Harvey P. Dale, May 12 2011 *)

A030154 Squares such that in n and sqrt(n) the parity of digits alternates.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 81, 256, 529, 729, 1296, 4761, 5476, 6561, 9216, 16129, 32761, 34969, 87616, 763876, 5414929, 5612161, 7414729, 7436529, 7634169, 14561856, 21058921, 34503876, 43072969, 43414921, 45252529, 69272329

Offset: 1

Patrick De Geest

The more digits there are in n, the lower the likelihood that the parity of n's digits will strictly alternate. Thus, the terms of the sequence become increasingly rare as n gets larger. - Harvey P. Dale, Aug 05 2018

For n > 3 the last digit of a(n) isn't 0 or 4. - David A. Corneth, Aug 05 2018

Andrew Howroyd, Table of n, a(n) for n = 1..1226 (first 101 terms from Harvey P. Dale, terms 102..223 from David A. Corneth)

Cf. A030141, A030151, A030152, A030153.

pdaQ[n_]:=Module[{a=Mod[IntegerDigits[n],2],b=Mod[IntegerDigits[ Sqrt[ n]],2]},Length[ Split[a]] ==IntegerLength[n]&&Length[Split[b]]== IntegerLength[ Sqrt[n]]]; Join[{0},Select[Range[8500]^2,pdaQ]] (* Harvey P. Dale, Aug 05 2018 *)

alternating(n)={my(v=digits(n)%2);0==#select(i->v[i]==v[i-1],[2..#v])}
{ for(n=0, 10^5, if(alternating(n^2) && alternating(n), print1(n^2, ", "))) } \\ Andrew Howroyd, Aug 05 2018

\\ for larger n: requires alternating function above
upto(n)={local(R=List([0])); my(recurse(s,b)=if(b0&&alternating(k^2\b), listput(R, k)); self()(k, 10*b)))))); recurse(0,1); listsort(R); Vec(R)}
apply(n->n^2, upto(sqrtint(10^12))) \\ Andrew Howroyd, Aug 05 2018

Offset changed by David A. Corneth, Aug 05 2018

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A030152 Squares in which parity of digits alternates.

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A030151 Numbers k such that in k^2 the parity of digits alternates.

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A030154 Squares such that in n and sqrt(n) the parity of digits alternates.

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