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... stochastic rounding: this rounding method requires the aid of a random number generator. Rounding of r may be done using any of the above methods when r is not exactly half way between two consecutive integers. Otherwise, r is randomly rounded up or down based on the outcome of randomly selecting a ...
... stochastic rounding: this rounding method requires the aid of a random number generator. Rounding of r may be done using any of the above methods when r is not exactly half way between two consecutive integers. Otherwise, r is randomly rounded up or down based on the outcome of randomly selecting a ...
Recursive call to factorial(1)
... In this example, we observe that we only need to know the last two computed values in order to compute the next value This follows directly from the recurrence relation ...
... In this example, we observe that we only need to know the last two computed values in order to compute the next value This follows directly from the recurrence relation ...
Explicit estimates for the distribution of numbers free of large prime
... We can take H = 3 · 1010 , see Platt [16]. Thus, we have the result in the range 1019 ≤ x ≤ e45 . For x ≥ e45 we have from Büthe [5] that |ψ(x)−x|/x ≤ 1.118·10−8 . Further, we have (see [18, (3.39)]) for x > 0, ψ(x) ≥ ϑ(x) > ψ(x) − 1.02x1/2 − 3x1/3 . (This result can be improved, but it is not impo ...
... We can take H = 3 · 1010 , see Platt [16]. Thus, we have the result in the range 1019 ≤ x ≤ e45 . For x ≥ e45 we have from Büthe [5] that |ψ(x)−x|/x ≤ 1.118·10−8 . Further, we have (see [18, (3.39)]) for x > 0, ψ(x) ≥ ϑ(x) > ψ(x) − 1.02x1/2 − 3x1/3 . (This result can be improved, but it is not impo ...
34(2)
... where m + n + p + q = 1 (mod 2) and (m, n, p, q) = 1. In the formulas above, either three or four variables are needed to generate four other integers (a, b,c,d). In this paper, we present 2-parameter Pythagorean quadruple formulas where the two integral parameters are also part of the solution set. ...
... where m + n + p + q = 1 (mod 2) and (m, n, p, q) = 1. In the formulas above, either three or four variables are needed to generate four other integers (a, b,c,d). In this paper, we present 2-parameter Pythagorean quadruple formulas where the two integral parameters are also part of the solution set. ...
Fibonacci numbers
... Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many.[29] Fkn is divisible by Fn, so, apart from F4 = 3, any Fibonacci prime must have a prime index. As there are arbitrarily long runs of composite numbers, there are therefore also arbitrar ...
... Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many.[29] Fkn is divisible by Fn, so, apart from F4 = 3, any Fibonacci prime must have a prime index. As there are arbitrarily long runs of composite numbers, there are therefore also arbitrar ...
The Math Encyclopedia of Smarandache Type Notions / Vol. 1
... 2)*n if m is even (respectively, by convention, n!! = 1 if n = 0); the congruence modulo: m is congruent modulo x with n and it is noted m ≡ n (mod x) if the remainder of the division of m by x is equal to the remainder of the division of n by x, for instance 17 ≡ 5 (mod 3); the primorial: this func ...
... 2)*n if m is even (respectively, by convention, n!! = 1 if n = 0); the congruence modulo: m is congruent modulo x with n and it is noted m ≡ n (mod x) if the remainder of the division of m by x is equal to the remainder of the division of n by x, for instance 17 ≡ 5 (mod 3); the primorial: this func ...
10 DECIMALS print
... Look one place to the right. What number is there? Compare the number to 5: 2 < 5 “stay” (keep) Keep the 8 and zero out the rest 22.68259 rounded to the nearest hundredths place is 22.68000 = 22.68 ...
... Look one place to the right. What number is there? Compare the number to 5: 2 < 5 “stay” (keep) Keep the 8 and zero out the rest 22.68259 rounded to the nearest hundredths place is 22.68000 = 22.68 ...
10 decimals
... Look one place to the right. What number is there? Compare the number to 5: 2 < 5 “stay” (keep) Keep the 8 and zero out the rest 22.68259 rounded to the nearest hundredths place is 22.68000 = 22.68 ...
... Look one place to the right. What number is there? Compare the number to 5: 2 < 5 “stay” (keep) Keep the 8 and zero out the rest 22.68259 rounded to the nearest hundredths place is 22.68000 = 22.68 ...