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A285269
Number of (odd) primes between 2*n^2 and 2*(n+1)^2.
0
0, 3, 3, 4, 4, 5, 5, 6, 6, 9, 7, 8, 7, 9, 10, 10, 9, 12, 10, 11, 13, 11, 14, 13, 14, 13, 14, 16, 16, 15, 15, 16, 17, 18, 19, 14, 22, 19, 18, 16, 22, 18, 24, 20, 22, 22, 20, 23, 24, 22, 23, 21, 25, 27, 24, 27, 26, 25, 27, 25, 23, 33, 28, 25, 29, 28, 31, 30, 33, 29
OFFSET
0,2
COMMENTS
Essentially the same as A285786, except for the offset and initial values.
FORMULA
a(n) = A285786(n+1), for all n >= 2.
First differences of A278114, a(n) = A278114(n+1) - A278114(n), for n > 0.
EXAMPLE
a(0) = 0 because between 2*0^2 = 0 and 2*1^2 = 2, there are no (odd) primes.
a(1) = 3 because between 2*1^2 = 2 and 2*2^2 = 8 there are the 3 (odd) primes 3, 5 and 7.
a(2) = 3 because between 2*2^2 = 8 and 2*3^2 = 18] there are the 3 primes 11, 13 and 17.
PROG
(PARI) a(n)=primepi(2*(n+1)^2-1)-primepi(2*n^2)
CROSSREFS
Sequence in context: A134993 A011375 A119661 * A285786 A120196 A196179
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 02 2017
STATUS
approved