A246972 -id:A246972 - cp's OEIS frontend

A104301 Primes which are the reverse concatenation of two consecutive square numbers.

41, 6449, 196169, 576529, 11561089, 14441369, 27042601, 38443721, 51845041, 60845929, 67246561, 84648281, 1081610609, 2073620449, 2190421609, 2822427889, 3240032041, 4000039601, 4326442849, 5017649729, 5290052441, 6250062001, 7507674529, 8294482369, 103684103041

Offset: 1

Shyam Sunder Gupta, Apr 17 2005

			The first term is 41 which is a prime and is the reverse concatenation of 1 and 4 which are two consecutive square numbers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

These are the primes in A246972.

Cf. A104242, A104302, A104303, A104304.

cat[s_] := FromDigits[Flatten[IntegerDigits[s]]]; Select[cat /@ Reverse /@ Partition[Range[350]^2, 2, 1], PrimeQ] (* Amiram Eldar, Jul 15 2025 *)

from sympy import isprime
A104301_list = []
for n in range(1, 2000):
    x = int(str((n+1)**2)+str(n**2))
    if isprime(x):
        A104301_list.append(x) # 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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A104301 Primes which are the reverse concatenation of two consecutive square numbers.

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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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Magma

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

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