login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065796 Alternating sum of digits of n^2. 3
1, 4, 9, 5, 3, 3, 5, -2, -7, 1, 0, 1, 4, -2, 5, 3, 3, 5, -2, 4, 1, 0, 12, 4, 9, 5, 14, 3, 5, 9, 4, 1, 0, 1, 4, -2, 5, 3, 3, 5, -2, 4, 12, 11, 1, 4, 9, 5, 3, 3, 5, 9, 15, 12, 0, 1, 4, -2, -6, 3, 3, 5, 9, -7, 1, 0, 1, 4, -2, 5, -8, -8, 5, -2, 4, 1, 11, -10, -7, -2, -6, 3, 3, -6, -2, -7, 1, 0, 1, -7, -13, -6, 3, 3, -6, -2, 4, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture; there are an infinite number of values which do not appear in this sequence (in the signed version, of course). The first example appears to be 2. Sean A. Irvine has checked this up to 10^9. - Robert G. Wilson v, Dec 10 2001

a(n) == n^2 (mod 11).  In particular, values == 2, 6, 7, 8, 10 (mod 11) do not appear, and the conjecture is true. - Robert Israel, Oct 24 2017

LINKS

Harry J. Smith, Table of n, a(n) for n=1..1000

FORMULA

a(n) = n^2 mod 10 - n^2 mod 100 div 10 + n^2 mod 1000 div 100 - ...

a(n) = A055017(n^2). - Robert Israel, Oct 24 2017

EXAMPLE

a(18)=5 because 18^2 is 324 and 4-2+3=5

MAPLE

asd:= proc(n) local L, j;

  L:= convert(n, base, 10);

  add((-1)^(j+1)*L[j], j=1..nops(L))

end proc:

seq(asd(n^2), n=1..100); # Robert Israel, Oct 24 2017

MATHEMATICA

f[n_] := Block[ {d = Reverse[ IntegerDigits[ n]], k = l = 1, s = 0}, l = Length[d]; While[ k <= l, s = s - (-1)^k*d[[k]]; k++ ]; Return[s]]; Table[ f[n^2], {n, 1, 100} ]

Table[Total[Times@@@Partition[Riffle[IntegerDigits[n^2], {1, -1}, {-2, 1, -2}], 2]], {n, 1, 100}] (* Vincenzo Librandi, Oct 24 2017 *)

PROG

(PARI) SumAD(x)= { local(a=1, s=0); while (x>9, s+=a*(x-10*(x\10)); x\=10; a=-a); return(s + a*x) }

{ for (n=1, 1000, write("b065796.txt", n, " ", SumAD(n^2)) ) } \\ Harry J. Smith, Oct 30 2009

CROSSREFS

Cf. A055017.

Sequence in context: A200396 A011513 A164818 * A070434 A011003 A200011

Adjacent sequences:  A065793 A065794 A065795 * A065797 A065798 A065799

KEYWORD

base,easy,sign

AUTHOR

Benny Wegner (jaeger(AT)clan-efg.de), Dec 05 2001

EXTENSIONS

More terms from Robert G. Wilson v, Dec 06 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 04:28 EDT 2019. Contains 328145 sequences. (Running on oeis4.)