A115439 -id:A115439 - cp's OEIS frontend

A115447 Numbers whose square is the concatenation of two numbers k and k-9.

71, 7235, 9701, 798981, 997001, 35324118, 64675883, 99970001, 3297392379, 6702607622, 7890726434, 8812181189, 9999700001, 897807218979, 917811219179, 979998999801, 999997000001, 46193210013657, 49751928874867

Offset: 1

Giovanni Resta, Jan 25 2006

			638370_638361 = 798981^2.

Cf. A030467, A106497, A115436, A115427, A115438, A115439, A115440, A115441, A115442, A115443, A115444, A115445, A115446.

A340231 Numbers of the form m^2-4 and also equal to some k concatenated with k+1.

Original entry on oeis.org

12, 45, 2021, 3132, 1456414565, 3823938240, 6991969920, 120395120396, 426436426437, 902596902597, 74780207478021, 90902209090221, 66713320846671332085, 81142640598114264060, 84822272598482227260, 99002509969900250997, 22443387868362244338786837, 24905771529642490577152965

Offset: 1

Bernard Schott, Jan 01 2021

All the terms have an even number of digits, but there is no term with 6, 8, 16, 18, 22, 24, ... digits.
The values of m are A115439, because a(n) = m^2-4 and a(n) = k|k+1 <==> a(n)+4 = m^2 and a(n)+4 = k|k+5 <==> m^2 = k|k+5, where | denotes concatenation.
a(3) = 2021 = 43*47 is A143206(6), the product of a cousin prime pair.
The next such term is A115439(1062)^2 - 4. - David A. Corneth, Jan 02 2021

			a(1) = 12 = 4^2-4 = 2*6.
a(4) = 3132 = 56^2-4 = 54*58.

Intersection of A001704 and A028347.

Cf. A115439, A143206.

Select[Table[n 10^IntegerLength[n]+n+1,{n,10^6}],IntegerQ[Sqrt[#+4]]&] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Dec 27 2022 *)

def agen():
  m = 4
  while True:
    tstr = str(m*m-4)
    k = int(tstr[:len(tstr)//2])
    if tstr == str(k) + str(k+1):
      yield(int(tstr))
    m += 1
for an in agen(): print(an, end=", ") # Michael S. Branicky, Jan 02 2021

a(13)-a(16) from Michael S. Branicky, Jan 02 2021

a(17)-a(18) from David A. Corneth, Jan 02 2021

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A115447 Numbers whose square is the concatenation of two numbers k and k-9.

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A340231 Numbers of the form m^2-4 and also equal to some k concatenated with k+1.

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