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 1-5 of 5 results.

A019550 a(n) is the concatenation of n and 2n.

Original entry on oeis.org

12, 24, 36, 48, 510, 612, 714, 816, 918, 1020, 1122, 1224, 1326, 1428, 1530, 1632, 1734, 1836, 1938, 2040, 2142, 2244, 2346, 2448, 2550, 2652, 2754, 2856, 2958, 3060, 3162, 3264, 3366, 3468, 3570, 3672, 3774, 3876, 3978, 4080, 4182, 4284, 4386, 4488, 4590
Offset: 1

Views

Author

R. Muller

Keywords

Comments

Concatenation of digits of n and 2*n. - Harvey P. Dale, Sep 13 2011
All terms are divisible by 6. - Robert Israel, Sep 21 2015

Links

Crossrefs

Cf. concatenation of n and k*n: A020338 (k=1), this sequence (k=2), A019551 (k=3), A019552 (k=4), A019553 (k=5), A009440 (k=6), A009441 (k=7), A009470 (k=8), A009474 (k=9).
Cf. A235497.
Supersequence of A117304.

Programs

  • Magma
    [Seqint(Intseq(2*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014
  • Maple
    seq(n*(10^(1+ilog10(2*n))+2),n=1..100); # Robert Israel, Sep 21 2015
  • Mathematica
    nxt[n_]:=Module[{idn=IntegerDigits[n],idn2=IntegerDigits[2n]}, FromDigits[ Join[ idn,idn2]]]; Array[nxt,40] (* Harvey P. Dale, Sep 13 2011 *)
  • PARI
    a(n) = eval(Str(n, 2*n)); \\ Michel Marcus, Sep 21 2015
  • Python
    def a(n): return int(str(n) + str(2*n))
print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Dec 24 2021

Formula

From Robert Israel, Sep 21 2015 (Start)
G.f.: (6*(2*x+75*x^5-60*x^6) + 90*Sum_{k>=1} 10^k*x^(5*10^k)*(5*10^k - (5*10^k-1)*x))/(1-x)^2.
a(n+2) - 2*a(n+1) + a(n) = 45*10^(2*k+1) if n = 5*10^k-2, 90*10^k-450*10^(2*k) if n = 5*10^k-1, 0 otherwise. (End)

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Feb 04 2014

A246972 (n+1)^2 concatenated with n^2.

Original entry on oeis.org

10, 41, 94, 169, 2516, 3625, 4936, 6449, 8164, 10081, 121100, 144121, 169144, 196169, 225196, 256225, 289256, 324289, 361324, 400361, 441400, 484441, 529484, 576529, 625576, 676625, 729676, 784729, 841784, 900841, 961900, 1024961, 10891024, 11561089, 12251156, 12961225, 13691296
Offset: 0

Views

Author

N. J. A. Sloane, Sep 13 2014

Keywords

Links

Crossrefs

Cf. A246973, A235497. For primes, see A104301.

Programs

  • Magma
    [10] cat [Seqint(Intseq(n^2) cat Intseq(n^2+2*n+1)): n in [1..50]]; // Vincenzo Librandi, Sep 13 2014
  • Mathematica
    Table[FromDigits[Join[Flatten[IntegerDigits[{(n + 1)^2, n^2}]]]], {n, 0, 50}] (* Vincenzo Librandi, Sep 13 2014 *)
FromDigits/@(Join[IntegerDigits[#[[2]]],IntegerDigits[#[[1]]]]&/@ Partition[ Range[0,40]^2,2,1]) (* Harvey P. Dale, Apr 16 2015 *)
  • Python
    def A246972(n):
    return int(str((n+1)**2)+str(n**2)) # Chai Wah Wu, Sep 13 2014

A246973 n^2 concatenated with (n+1)^2.

Original entry on oeis.org

1, 14, 49, 916, 1625, 2536, 3649, 4964, 6481, 81100, 100121, 121144, 144169, 169196, 196225, 225256, 256289, 289324, 324361, 361400, 400441, 441484, 484529, 529576, 576625, 625676, 676729, 729784, 784841, 841900, 900961, 9611024, 10241089, 10891156, 11561225, 12251296, 12961369, 13691444
Offset: 0

Views

Author

N. J. A. Sloane, Sep 13 2014

Keywords

Examples

			a(2) = 49 because 2^2 = 4 and 3^2 = 9.
a(3) = 916 because 3^2 = 9 and 4^2 = 16.
a(4) = 1625 because 4^2 = 16 and 5^2 = 25.

Links

Crossrefs

For primes see A104242.
Cf. A235497.

Programs

  • Magma
    [1] cat [Seqint(Intseq(n^2+2*n+1) cat Intseq(n^2)): n in [1..50]]; // Vincenzo Librandi, Sep 13 2014
  • Maple
    a:= n-> parse(cat(n^2, (n+1)^2)):
seq(a(n), n=0..40);  # Alois P. Heinz, May 27 2018
  • Mathematica
    Table[FromDigits[Join[IntegerDigits[n^2], IntegerDigits[(n + 1)^2]]], {n, 0, 39}] (* Alonso del Arte, Sep 13 2014 *)
  • PARI
    a(n) = eval(Str(n^2,(n+1)^2)) \\ Michel Marcus, Sep 13 2014 and M. F. Hasler, May 27 2018
  • PARI
    A246973(n)=n^2*10^logint(10*(n+1)^2,10)+(n+1)^2 \\ Over 4 x faster than using eval(Str(...)). - M. F. Hasler, May 27 2018

A247337 a(n) = Lucas(n) concatenated with Fibonacci(n).

Original entry on oeis.org

20, 11, 31, 42, 73, 115, 188, 2913, 4721, 7634, 12355, 19989, 322144, 521233, 843377, 1364610, 2207987, 35711597, 57782584, 93494181, 151276765, 2447610946, 3960317711, 6407928657, 10368246368, 16776175025, 271443121393, 439204196418, 710647317811, 1149851514229
Offset: 0

Views

Author

Vincenzo Librandi, Sep 14 2014

Keywords

Links

Crossrefs

Cf. A000032, A000045, A235497, A246972, A246973.

Programs

  • Magma
    [20] cat [Seqint(Intseq(Fibonacci(n)) cat Intseq(Lucas(n))): n in [1..50]];
  • Mathematica
    Table[FromDigits[Join[Flatten[IntegerDigits[{LucasL[n], Fibonacci[n]}]]]], {n, 0, 50}]

A247338 a(n) = Fibonacci(n) concatenated with Lucas(n).

Original entry on oeis.org

2, 11, 13, 24, 37, 511, 818, 1329, 2147, 3476, 55123, 89199, 144322, 233521, 377843, 6101364, 9872207, 15973571, 25845778, 41819349, 676515127, 1094624476, 1771139603, 2865764079, 46368103682, 75025167761, 121393271443, 196418439204, 317811710647, 5142291149851
Offset: 0

Views

Author

Vincenzo Librandi, Sep 14 2014

Keywords

Links

Crossrefs

Cf. A000032, A000045, A235497, A246972, A246973.

Programs

  • Magma
    [Seqint(Intseq(Lucas(n)) cat Intseq(Fibonacci(n))): n in [0..50]];
  • Mathematica
    Table[FromDigits[Join[Flatten[IntegerDigits[{Fibonacci[n], LucasL[n]}]]]], {n, 0, 50}]
  • PARI
    a(n)=eval(Str(fibonacci(n),fibonacci(n-1)+fibonacci(n+1))) \\ Charles R Greathouse IV, Sep 14 2014
Showing 1-5 of 5 results.

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

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