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A374846
Numbers appearing exactly once in a Pythagorean triple.
1
3, 4, 6, 7, 11, 14, 19, 22, 23, 31, 38, 43, 46, 47, 59, 62, 67, 71, 79, 83, 86, 94, 103, 107, 118, 127, 131, 134, 139, 142, 151, 158, 163, 166, 167, 179, 191, 199, 206, 211, 214, 223, 227, 239, 251, 254, 262, 263, 271, 278, 283, 302, 307, 311, 326, 331, 334, 347, 358, 359, 367, 379, 382, 383, 398
OFFSET
1,1
COMMENTS
Positions of the ones in A046081.
With the exception a(2) = 4, the terms are given by A374845, thus providing a simple formula for the sequence.
LINKS
A. Tripathi, On Pythagorean triples containing a fixed integer, Fib. Q., 46/47 (2008/2009), 331-340. See Theorem 8.
FORMULA
p or 2p with p prime and p = 3 mod 4, with 4 added to the sequence, in ascending order.
MATHEMATICA
t={}; Do[If[(PrimeQ[n] && Mod[n, 4] == 3) || (PrimeQ[n/2] && Mod [n/2, 4] == 3), t = Join[t, {n}]], {n, 445}]; t = Insert[t, 4, 2]
(* Positions of the ones in A046081; based on program by Jean-François Alcover *)
a[1] = 0; a[n_] := Module[{f}, f = Select[FactorInteger[n], Mod[#[[1]], 4] == 1 &][[All, 2]]; (DivisorSigma[0, If[OddQ[n], n, n/2]^2] - 1)/2 + (Times @@ (2*f + 1) - 1)/2]; arr = Array[a, 445]; fl = Flatten[Position[arr, 1]]
PROG
(Python)
from itertools import count, islice
from sympy import isprime
def A374846_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:n==4 or (isprime(n) and n&3==3) or (isprime(n>>1) and n&7==6), count(max(startvalue, 1)))
A374846_list = list(islice(A374846_gen(), 20)) # Chai Wah Wu, Jul 31 2024
CROSSREFS
Sequence in context: A075434 A085253 A207525 * A240208 A349555 A073906
KEYWORD
nonn
AUTHOR
Manfred Boergens, Jul 22 2024
STATUS
approved