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.

A191933 Numbers that are the concatenation of the decimal representation of two nonzero squares.

Original entry on oeis.org

11, 14, 19, 41, 44, 49, 91, 94, 99, 116, 125, 136, 149, 161, 164, 169, 181, 251, 254, 259, 361, 364, 369, 416, 425, 436, 449, 464, 481, 491, 494, 499, 641, 644, 649, 811, 814, 819, 916, 925, 936, 949, 964, 981, 1001, 1004, 1009, 1100, 1121, 1144, 1169, 1196
Offset: 1

Views

Author

Klaus Brockhaus, Jun 19 2011

Keywords

Comments

Complement of A193096; A193095(a(n)) > 0; A038670, A039686, A167535, A192993, A193097 and A193144 are subsequences. [Reinhard Zumkeller, Jul 17 2011]

Links

Crossrefs

Cf. A000290, A192993.

Programs

  • Haskell
    import Data.List (findIndices)
a191933 n = a191933_list !! (n-1)
a191933_list = findIndices (> 0) $ map a193095 [0..]
-- Reinhard Zumkeller, Jul 17 2011
  • Magma
    CheckSplits:=function(n); v:=false; S:=Intseq(n); for j in [1..#S-1] do A:=[ S[k]: k in [1..j] ]; a:=Seqint(A); B:=[ S[k]: k in [j+1..#S] ]; b:=Seqint(B); if a gt 0 and A[#A] gt 0 and IsSquare(a) and IsSquare(b) then v:=true; end if; end for; return v; end function; [ p: p in [1..1200] | CheckSplits(p) ];
  • Mathematica
    Take[Union[Flatten[Table[FromDigits[Flatten[{IntegerDigits[m^2], IntegerDigits[n^2]}]], {m, 20}, {n, 20}]]], 50] (* Alonso del Arte, Aug 11 2011 *)
squareQ[n_] := IntegerQ[Sqrt[n]]; okQ[n_] := MatchQ[IntegerDigits[n], {a__ /; squareQ[FromDigits[{a}]], b__ /; First[{b}] > 0 && squareQ[FromDigits[ {b}]]}]; Select[Range[2000], okQ] (* Jean-François Alcover, Dec 13 2016 *)

A193095 Number of times n can be written as concatenation of exactly two nonzero squares in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 17 2011

Keywords

Comments

a(A193096(n))=0; a(A191933(n))>0; a(A193097(n))=1; a(A192993(n))>1; a(A038670(n))=2.

Examples

			a(164) = 2, A191933(15) = A192993(1) = 164: 1'64 == 16'4.

Links

Crossrefs

Cf. A010052.

Programs

  • Haskell
    a193095 n = sum $ map c [1..(length $ show n) - 1] where
   c k | head ys == '0' = 0
       | otherwise      = a010052 (read xs) * a010052 (read ys) where
       (xs,ys) = splitAt k $ show n
  • PARI
    A193095(n) = sum( t=1,#Str(n)-1, apply(issquare,divrem(n,10^t))==[1,1]~ && n%10^t>=10^(t-1))  \\ M. F. Hasler, Jul 24 2011
  • PARI
    A193095(n)={ my(c,p=1); while( n>p*=10, n%p*10>=p||next; issquare(n%p)||next; issquare(n\p) && c++);c}  \\ M. F. Hasler, Jul 24 2011

A192993 Numbers that are in more than one way the concatenation of the decimal representation of two nonzero squares.

Original entry on oeis.org

164, 1441, 1625, 1961, 2564, 4841, 12116, 14449, 16400, 25625, 46241, 48464, 115625, 116641, 144100, 148841, 160025, 162500, 163844, 169169, 184964, 193636, 196100, 256400, 361225, 368649, 466564, 484100, 493025, 961009, 973441, 1166464
Offset: 1

Views

Author

Klaus Brockhaus and Zak Seidov, Jul 14 2011

Keywords

Comments

Subsequence of A191933.
If k is a term, then k followed by two zeros is also a term.
None of the terms < 40000000 is in more than two ways the concatenation of the decimal representation of two nonzero squares.
A038670 is a subsequence. - Reinhard Zumkeller, Jul 15 2011

Examples

			2564 is the concatenation of 256 and 4 as well as of 25 and 64; 256, 4, 25, 64 are squares, so 2564 is a term.

Links

Crossrefs

Cf. A000290, A191933.

Programs

  • Haskell
    import Data.List (findIndices)
a192993 n = a192993_list !! (n-1)
a192993_list = findIndices (> 1) $ map a193095 [0..]
-- Reinhard Zumkeller, Jul 17 2011
  • Magma
    SplitToSquares:=function(n); V:=[]; S:=Intseq(n); for j in [1..#S-1] do A:=[ S[k]: k in [1..j] ]; a:=Seqint(A); B:=[ S[k]: k in [j+1..#S] ]; b:=Seqint(B); if a gt 0 and A[#A] gt 0 and IsSquare(a) and IsSquare(b) then Append(~V, []); end if; end for; return V; end function; [ p: p in [1..1200000] | #P gt 1 where P is SplitToSquares(p) ]; /* to obtain the splittings replace " p: " with " : " */
  • Mathematica
    f@n_ := DeleteDuplicates@
  Select[First@# & /@
    Select[Partition[
      Sort@(FromDigits@Flatten@IntegerDigits@# & /@
         Tuples[Range@Sqrt[10^(n - 1) - 1]^2, {2}]), 2, 1],
     Differences@# == {0} &], # <
10^n &]; f@7 (* Hans Rudolf Widmer, Jun 12 2023 *) (* Numbers with at most n digits that are in more than one way the concatenation of the decimal representation of two nonzero squares. *)
Showing 1-3 of 3 results.

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

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