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A340231
Numbers of the form m^2-4 and also equal to some k concatenated with k+1.
0
12, 45, 2021, 3132, 1456414565, 3823938240, 6991969920, 120395120396, 426436426437, 902596902597, 74780207478021, 90902209090221, 66713320846671332085, 81142640598114264060, 84822272598482227260, 99002509969900250997, 22443387868362244338786837, 24905771529642490577152965
OFFSET
1,1
COMMENTS
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
EXAMPLE
a(1) = 12 = 4^2-4 = 2*6.
a(4) = 3132 = 56^2-4 = 54*58.
MATHEMATICA
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 *)
PROG
(Python)
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
CROSSREFS
Intersection of A001704 and A028347.
Sequence in context: A331764 A372500 A249923 * A100183 A050490 A169881
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jan 01 2021
EXTENSIONS
a(13)-a(16) from Michael S. Branicky, Jan 02 2021
a(17)-a(18) from David A. Corneth, Jan 02 2021
STATUS
approved