cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A080151 Let m = Wonderful Demlo number A002477(n); a(n) = sum of digits of m.

Original entry on oeis.org

1, 4, 9, 16, 25, 36, 49, 64, 81, 82, 85, 90, 97, 106, 117, 130, 145, 162, 163, 166, 171, 178, 187, 198, 211, 226, 243, 244, 247, 252, 259, 268, 279, 292, 307, 324, 325, 328, 333, 340, 349, 360, 373, 388, 405, 406, 409, 414, 421, 430, 441, 454, 469, 486, 487
Offset: 1

Views

Author

Eric W. Weisstein, Jan 31 2003

Keywords

Comments

Record values in A003132. - Reinhard Zumkeller, Jul 10 2011

Links

Crossrefs

Cf. A080150, A002477, A080160, A080161, A080162.

Programs

  • Haskell
    a n=(div n 9)*81+(mod n 9)^2
          A080151=map a [1..] \\ Chernin Nadav, Mar 06 2014
  • Maple
    f := n -> 9*n - 81*frac(1/9*n) + 81*frac(1/9*n)^2:
map(f, [$1..100]); # Robert Israel, Aug 05 2019
  • Mathematica
    (* by direct counting *)
Repunit[n_] := (-1 + 10^n)/9; A080151[n_]:=Plus @@ IntegerDigits[Repunit[n]^2];
(* by the formula *)
A080151[n_] := (9^2)*(n/9 - FractionalPart[n/9] + FractionalPart[n/9]^2)
(* or alternatively *)
A080151[n_] := 81*(Floor[n/9]+ FractionalPart[n/9]^2) (* Enrique Pérez Herrero, Nov 22 2009 *)
  • PARI
    vector(100, n, (n\9)*81+(n%9)^2) \\ Colin Barker, Mar 05 2014

Formula

a(n) = A007953(A002477(n)).
a(n) = sqrt( A080150(n) ).
a(n) = (9^2)*(n/9 - {n/9} + {n/9}^2) = 81*(floor(n/9) + {n/9}^2), where the symbol {n} means fractional part of n. - Enrique Pérez Herrero, Nov 22 2009
a(n) = A003132(A051885(n)). - Reinhard Zumkeller, Jul 10 2011
a(9*n + k) = 81*n + k^2, with k in range 0 to 9. - Enrique Pérez Herrero, Nov 05 2022
Empirical g.f.: x*(17*x^8 + 15*x^7 + 13*x^6 + 11*x^5 + 9*x^4 + 7*x^3 + 5*x^2 + 3*x + 1) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Mar 05 2014
Empirical g.f. confirmed. - Robert Israel, Aug 05 2019

A080160 Squares that are digit sums of Wonderful Demlo numbers A002477.

Original entry on oeis.org

1, 4, 9, 16, 25, 36, 49, 64, 81, 324, 441, 576, 729, 900, 1089, 1296, 2025, 2304, 2601, 2916, 3249, 3600, 3969, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 9801, 10404, 11025, 11664
Offset: 1

Views

Author

N. J. A. Sloane, Jun 19 2005

Keywords

Comments

These are the squares in A080151.
x^2 is a term iff x mod 81 is in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 21, 24, 27, 30, 33, 36, 45, 48, 51, 54, 57, 60, 63, 72, 73, 74, 75, 76, 77, 78, 79, 80}. - Robert Israel, Jul 30 2025

Links

Crossrefs

Cf. A002477, A080151, A080161, A080162.
Cf. A007953.

Programs

  • Maple
    b:=n->sum(convert(((10^(n+1)-1)/9)^2,base,10)[j],j=1..2*n+1): a:=proc(n) if type(sqrt(b(n)),integer)=true then b(n) else fi end: seq(a(n),n=0..2000); # Emeric Deutsch, Jun 19 2005
  • Mathematica
    A080151[n_] := (9^2)*(n/9 - FractionalPart[n/9] + FractionalPart[n/9]^2)
A080151[Select[Range[10000], IntegerQ[Sqrt[A080151[#]]] &]]
(* Enrique Pérez Herrero, Nov 05 2022 *)

Extensions

More terms from Emeric Deutsch, Jun 19 2005

A080162 Wonderful Demlo numbers A002477 whose digit sums are squares.

Original entry on oeis.org

1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 12345679012345679012345679012345678987654320987654320987654320987654321
Offset: 1

Views

Author

Eric W. Weisstein, Jan 31 2003

Keywords

Comments

The next term (a(11)) has 101 digits. - Harvey P. Dale, Jun 16 2025

Links

Crossrefs

Cf. A080160, A080161, A002477, A080151.

Programs

  • Mathematica
    Select[LinearRecurrence[{111,-1110,1000},{1,121,12321},40],IntegerQ[Sqrt[Total[IntegerDigits[#]]]]&] (* Harvey P. Dale, Jun 16 2025 *)
  • PARI
    for(k=1,100,my(d=((10^k-1)/9)^2); issquare(sumdigits(d)) && print1(d,", ")) \\ Jeppe Stig Nielsen, May 27 2023
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.