A246973 -id:A246973 - cp's OEIS frontend

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

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

N. J. A. Sloane, Sep 13 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

[10] cat [Seqint(Intseq(n^2) cat Intseq(n^2+2*n+1)): n in [1..50]]; // Vincenzo Librandi, Sep 13 2014

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 *)

def A246972(n):
    return int(str((n+1)**2)+str(n**2)) # Chai Wah Wu, Sep 13 2014

A104242 Primes which are the concatenation of two consecutive square numbers.

Original entry on oeis.org

6481, 144169, 324361, 400441, 784841, 16001681, 23042401, 67246889, 77447921, 84648649, 92169409, 96049801, 1254412769, 1638416641, 1742417689, 1960019881, 2016420449, 4752447961, 5382454289, 5664457121, 5760058081, 6051661009

Offset: 1

Shyam Sunder Gupta, Apr 17 2005

The second prime in this sequence, 144169, arises in the theory of modular forms, as observed by Hecke. On page 671 of Hecke (1937), Hecke works out the cusp forms of weight 24 and observes that the Hecke operators have eigenfunctions with Fourier coefficients in the quadratic field of discriminant 144169. Thanks to Jerrold B. Tunnell for this comment. See also the articles by Hida and Zagier. N. J. A. Sloane, Sep 13 2014

			The first term is 6481 which is a prime and is the concatenation of 64 and 81 which are two consecutive square numbers.

E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung, Math. Annalen, 114 (1937), 1-28; Werke pp. 644-671. See page 671.

Robert Israel, Table of n, a(n) for n = 1..10000
Haruzo Hida, Arithmetic of Weil numbers and Hecke fields.
Don Zagier, Elliptic Modular Forms and Their Applications

A090738 gives the numbers n such that a(n) = (n^2 concatenated with (n+1)^2) is prime.

These are the primes in A246973. Cf. A104301, A246972.

catn:= proc(a,b) 10^(1+ilog10(b))*a+b end proc:
R:= NULL: count:= 0:
for x from 2 by 2 while count < 100 do
  y:= catn(x^2,(x+1)^2);
  if isprime(y) then count:= count+1; R:= R, y; fi
od:
R; # Robert Israel, May 19 2020

from sympy import isprime
A104242_list = []
for n in range(1,2000):
    x = int(str(n**2)+str((n+1)**2))
    if isprime(x):
        A104242_list.append(x) # Chai Wah Wu, Sep 13 2014

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

Vincenzo Librandi, Sep 14 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

[20] cat [Seqint(Intseq(Fibonacci(n)) cat Intseq(Lucas(n))): n in [1..50]];

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

Vincenzo Librandi, Sep 14 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

[Seqint(Intseq(Lucas(n)) cat Intseq(Fibonacci(n))): n in [0..50]];

Table[FromDigits[Join[Flatten[IntegerDigits[{Fibonacci[n], LucasL[n]}]]]], {n, 0, 50}]

a(n)=eval(Str(fibonacci(n),fibonacci(n-1)+fibonacci(n+1))) \\ Charles R Greathouse IV, Sep 14 2014

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

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A104242 Primes which are the concatenation of two consecutive square numbers.

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

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

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