A139221 Numbers k such that both 41+(k+k^2)/2 and 41+(k+k^2) are primes.
0, 3, 11, 20, 23, 27, 32, 39, 48, 51, 59, 60, 83, 108, 111, 116, 128, 132, 135, 171, 188, 203, 212, 227, 240, 263, 275, 315, 324, 356, 359, 363, 384, 392, 447, 476, 479, 515, 528, 588, 627, 647, 648, 672, 731, 759, 780, 804, 839, 864, 875, 900, 903, 968, 975
Offset: 1
Keywords
Examples
If k = 11 then 41 + (k + k^2) / 2 = 107 (prime) and 41 + (k + k^2) = 173 (prime).
Links
- Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Programs
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Magma
[k:k in [0..1000]| IsPrime(41+(k+k^2) div 2) and IsPrime(41+k+k^2)]; // Marius A. Burtea, Feb 12 2020
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Mathematica
Select[Table[Range[0,2000]],PrimeQ[41+(#+#^2)/2]&&PrimeQ[41+#+#^2]&] Select[Range[0,1000],AllTrue[41+{(#+#^2)/2,#+#^2},PrimeQ]&] (* Harvey P. Dale, May 21 2024 *) -
PARI
for(n=0, 1000, if(isprime(binomial(n+1,2) +41) && isprime(n^2+n+41), print1(n", "))) \\ G. C. Greubel, Feb 12 2020
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Sage
[n for n in (0..1000) if is_prime(binomial(n+1,2)+41) and is_prime(n^2+n+41)] # G. C. Greubel, Feb 12 2020
Comments