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A037073 Numbers k such that (6*k)^2 is the sum of a twin prime pair. 14
1, 2, 7, 8, 12, 14, 15, 29, 34, 44, 51, 62, 68, 76, 79, 91, 99, 100, 107, 125, 142, 147, 156, 162, 163, 173, 190, 202, 212, 231, 245, 252, 253, 264, 295, 306, 317, 330, 331, 355, 366, 376, 377, 386, 397, 442, 448, 453, 462, 469, 481, 491, 498, 502, 516, 547 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
C. K. Caldwell, Twin primes
FORMULA
a(n) = A173165(n)/3. - M. F. Hasler, Oct 30 2023
EXAMPLE
E.g. n=44 -> (6*44)^2 = 69696 = 34847 + 34849 (twin prime pair).
MAPLE
isa := n -> isprime(n) and isprime(n+2) and issqr(2*n+2):
select(isa, [$4..1000000]): map(n -> sqrt(2*n+2)/6, %); # Peter Luschny, Jan 05 2020
MATHEMATICA
Select[Sqrt[Plus@@@Select[Partition[Prime[Range[4*10^5]], 2, 1], Differences[#]=={2} &]/36], IntegerQ] (* Jayanta Basu, May 26 2013 *)
PROG
(PARI) is(n)=isprime(18*n^2-1)&&isprime(18*n^2+1) \\ M. F. Hasler, Oct 30 2023
CROSSREFS
A152786 = 6*A037073. - Zak Seidov, Aug 20 2010
Sequence in context: A053013 A070044 A129850 * A358535 A329407 A329408
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Jud McCranie, Dec 30 2000
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)