Download A set of new Smarandache functions, sequences and by Felice Russo PDF

By Felice Russo

Show description

Read or Download A set of new Smarandache functions, sequences and conjectures in number theory PDF

Similar theory books

Ginzburg-Landau Phase Transition Theory and Superconductivity

The speculation of advanced Ginzburg-Landau kind section transition and its applica­ tions to superconductivity and superfluidity has been an issue of serious curiosity to theoretical physicists and has been consistently and over and over studied because the Fifties. at the present time, there's an abundance of mathematical effects unfold over numer­ ous medical journals.

Plurality and Continuity: An Essay in G.F. Stout’s Theory of Universals

By way of D. M. Armstrong within the historical past of the dialogue of the matter of universals, G. F. Stout has an honoured, and precise. position. For the Nominalist, which means by means of that time period a thinker who holds that life of repeatables - varieties, kinds, style- and the indubitable life of normal phrases, is an issue.

Meter in Poetry : a New Theory

The 1st ebook to supply a common linguistic thought of poetic meter.

Additional info for A set of new Smarandache functions, sequences and conjectures in number theory

Sample text

4). Smarandache Mertens Function Power sequence 30 25 20 Sm(n) 15 10 5 0 -5 -10 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 n Mertens function sqrt(a(n)) Fig. 4 20) Smarandache Ramanujan Constant For any Smarandache sequence a(n) we can define the following function: 4 ⋅S SR = eπ ⋅ int(π ) where S = ∑ 1 and assuming that S converge. 728831.... 5336... 615792.... 99318... 913745.... 754... 513624.... 5587..... 239704.... 3... Problem 18. Is there any Smarandache sequence a(k) like the cubic-product one such that SR is close to an integer?

S ⋅ t − 1) But s ⋅ t − p ⋅ q = 1 being n and n+1 consecutive. This implies that = k but s ⋅t this is absurd because s ⋅ t − 1 and s ⋅ t don't have any common factor. So our initial assumption is false. Same thing for the equation 31 Zw( n + 1) =k. Zw(n) For case 2 without loss of generality let’s suppose that: n = p a ⋅ q b and n + 1 = sc ⋅ t d where p, q, s, t are distinct primes. 2, Zw (n) = p ⋅ q and Zw (n + 1) = s ⋅ t and then let’s s ⋅t suppose that =k. p⋅q Since s ⋅ t − p ⋅ q = 1 , being n and n+1 consecutive, m ⋅ s ⋅ t − m' ⋅ p ⋅ q = 1 where m and m' are two integers, because s c ⋅ t d and p a ⋅ q b are multiple of s ⋅ t and p ⋅ q respectively.

1, 1998, p. 149-151 [4] F. Russo, Some results about four Smarandache U-product sequences, Smarandache Notions Journal, Nov. 1999 [5] E. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 1999 [6] N. com/ ~njas/sequences/ 56 Chapter III A set of new Smarandache sequences. The greatest discovery of all humankind may well have been the natural numbers. For many past aeons, philosophers and mathematicians have studied the sequence of natural numbers, uncovering startling and mystifying truths.

Download PDF sample

Rated 4.82 of 5 – based on 16 votes