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A282319
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a(n) = (2097203 mod n)^2 + (2097203 mod n) + 41.
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1
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41, 43, 47, 53, 53, 71, 53, 53, 71, 53, 131, 173, 61, 53, 113, 53, 281, 71, 47, 53, 347, 131, 347, 173, 53, 347, 71, 53, 151, 593, 547, 421, 461, 281, 53, 593, 83, 503, 347, 53, 197, 347, 97, 1033, 593, 347, 313, 1301, 53, 53, 1097, 1933, 2203, 71
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OFFSET
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1,1
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COMMENTS
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This sequence gives 168 prime numbers for n=1 to 168 with 63 different primes. This formula is based on the lucky numbers of Euler.
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LINKS
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Table of n, a(n) for n=1..54.
Frederic Isenmann, Table of n, a(n) for n=1..168.
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EXAMPLE
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For n = 23, a(23) = 17^2+17+41 = 347, and 347 is prime.
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MATHEMATICA
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Table[#^2 + # + 41 &@ Mod[2097203 , n], {n, 54}] (* Michael De Vlieger, Feb 12 2017 *)
f[n_]:=Module[{x=Mod[2097203, n]}, x^2+x+41]; Array[f, 60] (* Harvey P. Dale, Jul 28 2017 *)
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PROG
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(Python)
def formul(i):
return ((i*i+2097203)%i)*((i*i+2097203)%i)+((i*i+2097203)%i)+41
for i in range(1, 169):
n=formul(i)
print(n, end=", ")
(PARI) a(n)=subst(x^2+x+41, x, 2097203%n) \\ Charles R Greathouse IV, Feb 14 2017
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CROSSREFS
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Cf. A005846, A202018.
Sequence in context: A073921 A118124 A054057 * A257362 A296921 A155884
Adjacent sequences: A282316 A282317 A282318 * A282320 A282321 A282322
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KEYWORD
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easy,nonn
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AUTHOR
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Frederic Isenmann, Feb 11 2017
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STATUS
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approved
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