A354499 Number of consecutive primes generated by adding 2n to the odd squares (A016754).
2, 4, 1, 0, 2, 1, 0, 1, 1, 0, 5, 0, 0, 3, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 14, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 4, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 0, 0, 0, 0, 8, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 3, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0
Offset: 1
Keywords
Examples
For n=1 we have 1^2+2*1=3 and 3^2+2*1=11 are prime but 5^2+2*1=27 is not, and thus a(1)=2. For n=2, 1^2+2*2=5 ... 7^2+2*2=53 are prime but 9^2+2*2=85 is not, thus a(2)=4. For n=3, 1^2+2*3=7 is prime but 3^2+2*3=15 is not thus a(3)=1. For n=4, 1^2+2*4=9 which is not prime, thus a(4)=0.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Maple
f:= proc(n) local k; for k from 1 by 2 do if not isprime(k^2+2*n) then return (k-1)/2 fi od end proc: map(f, [$1..100]); # Robert Israel, Oct 26 2023 -
Mathematica
a[n_] := Module[{k = 1}, While[PrimeQ[k^2 + 2*n], k += 2]; (k - 1)/2]; Array[a, 100] (* Amiram Eldar, Aug 15 2022 *) -
PARI
a(n) = my(k=1); while (isprime(k^2+2*n), k+=2); (k-1)/2; \\ Michel Marcus, Aug 16 2022
Formula
a(n) is number of consecutive primes generated by (2x-1)^2+2n for x=1,2,3,4,
Comments