A138337
Positions of digits after decimal point of number Pi where the approximation to the number Pi by a root of a polynomial of 3 degree does not improve the accuracy.
Original entry on oeis.org
7, 13, 17, 30, 37, 48, 62, 63, 77, 81, 86, 92, 97, 114, 117, 125, 129, 143, 148, 152, 156, 159, 168, 174, 180, 185, 196, 200, 204, 211, 227, 235, 244, 247, 259, 266, 267, 282
Offset: 1
a(1)=7 because 3.141593 (6 digits) is root of cubic 2 + 29 x - 22 x^2 + 4 x^3 and 3.1415927 (7 digits) also is root of that same polynomial -3061495+674903*x+95366*x^2
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b = {}; a = {}; Do[k = Recognize[N[Pi,n + 1], 3, x]; If[MemberQ[a, k], AppendTo[b, n], AppendTo[a, k]], {n, 2, 300}]; b
A243449
Primes of the form n^2 + 14.
Original entry on oeis.org
23, 239, 743, 1103, 2039, 5639, 7583, 8663, 27239, 33503, 38039, 42863, 59063, 81239, 88223, 91823, 119039, 131783, 140639, 164039, 189239, 205223, 245039, 263183, 288383, 328343, 342239, 378239, 393143, 400703, 431663, 439583, 514103, 660983, 710663, 950639
Offset: 1
Cf. primes of the form n^2+k:
A144255 (k=1),
A056899 (k=2),
A049423 (k=3),
A005473 (k=4),
A056905 (k=5),
A056909 (k=6),
A079138 (k=7),
A138338 (k=8),
A138353 (k=9),
A138355 (k=10),
A138362 (k=11),
A138368 (k=12),
A138375 (k=13), this sequence (k=14),
A243450 (k=15),
A243451 (k=16),
A228244 (k=17),
A174812 (k=42).
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[a: n in [0..1000] | IsPrime(a) where a is n^2+14];
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Select[Table[n^2 + 14, {n, 0, 2000}], PrimeQ]
Select[Range[1,1001,2]^2+14,PrimeQ] (* Harvey P. Dale, May 30 2023 *)
Showing 1-2 of 2 results.
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