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A228112 Difference between the number of primes with n digits (A006879) and the 6-parametric approximation of that number in A228111. 4
0, 0, 0, -2, -22, -23, 1614, 21952, 200754, 1427826, 6969680, -2536429, -648528610, -11247293516, -143493754330, -1578026921839, -15633412845816, -140582270611489, -1122913035234416, -7326349588043722, -25245049578998081, 301375487087871682, 9140885960557495580, 157255672291012140238, 2265259467069624459434 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A228111 provides exact values of pi(10^n)- pi(10^(n-1)) for n=1 to 3 and yields an average relative difference in absolute value, i.e. <ARD(A228112)> =Average(Abs(A228112(n))/ (A006879(n)) =3.75341...*10^-3 for 1<=n<=25, better than when using the ((10^n)/log(10^n)) function ( <ARD(A228066)> = 4.69094...*10^-2) or the Logarithm integral (Li(10^n)-Li(2)) function ( <ARD(A228068)> = 1.75492...*10^-2 ) or the Riemann (Riemann(10^n)) function (<ARD(A228114)> = 1.03936...*10^-2 ) or the Fibonacci polynomials of multiple of 4 indices (<ARD(A228064)> = 4.73860...*10^-3 ) for 1<=n<=25.

LINKS

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Prime-counting_function

Eric Weisstein's World of Mathematics, Fibonacci Polynomial.

FORMULA

a(n) = A006879(n)- A228111(n)

CROSSREFS

Cf. A006880, A006879, A228063, A228066, A228068, A228111, A228113, A228114, A228115, A228116

Sequence in context: A284063 A153826 A080283 * A080433 A022373 A111751

Adjacent sequences:  A228109 A228110 A228111 * A228113 A228114 A228115

KEYWORD

sign

AUTHOR

Vladimir Pletser, Aug 10 2013

STATUS

approved

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Last modified November 18 03:48 EST 2019. Contains 329248 sequences. (Running on oeis4.)