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A281437 Primes of the form 25*n^2 + 25*n + 47. 1
47, 97, 197, 347, 547, 797, 1097, 1447, 1847, 2297, 2797, 3347, 3947, 4597, 5297, 6047, 8597, 9547, 11597, 12697, 17597, 18947, 20347, 23297, 24847, 28097, 31547, 33347, 37097, 39047, 41047, 45197, 49547, 51797, 61297, 66347, 68947, 71597, 74297, 77047, 79847 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The first 16 terms correspond to n from 0 to 15, which makes 25*n^2 + 25*n + 47 a prime-generating polynomial (see the link).
This is a prime-generating polynomial of the form s*n^2 + s*n + p, where s=k^2 and p is prime with s and p containing at most two digits. Prime-generating polynomials of this kind arise for k=1,2,3,5,7. This is the case of k=5; it generates most primes in a row out of the prime k's listed, with 12 for k=3,7, and 14 for k=2. See also A005846 and A007635 (k=1), and A048988 (k=2).
All terms are of the form 10m+7, with their next-to-last digits being 4 or 9.
LINKS
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial
EXAMPLE
197 is a term as it is a prime corresponding to n=2: 25*4 + 25*2 + 47 = 197.
MATHEMATICA
Select[Range[0, 100]//25#^2+25#+47&, PrimeQ]
PROG
(PARI) for(n=0, 100, isprime(p=25*n^2+25*n+47)&& print1(p ", "))
CROSSREFS
Cf. A000040 (primes), A005846, A007635, A048988, A292578 (similar prime-generating sequences).
Sequence in context: A044566 A349231 A141944 * A319051 A180550 A176134
KEYWORD
nonn
AUTHOR
Waldemar Puszkarz, Oct 05 2017
STATUS
approved

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)