| Title:
|
Iterated digit sums, recursions and primality (English) |
| Author:
|
Ericksen, Larry |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
14 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
27-35 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We examine the congruences and iterate the digit sums of integer sequences. We generate recursive number sequences from triple and quintuple product identities. And we use second order recursions to determine the primality of special number systems. (English) |
| Keyword:
|
sum of digits |
| Keyword:
|
recursive sequences |
| Keyword:
|
triple product identity |
| Keyword:
|
quintuple product |
| Keyword:
|
primality testing |
| MSC:
|
11A07 |
| MSC:
|
11A51 |
| MSC:
|
11A63 |
| MSC:
|
11B37 |
| MSC:
|
11B39 |
| MSC:
|
11B50 |
| idZBL:
|
Zbl 1148.11007 |
| idMR:
|
MR2298910 |
| . |
| Date available:
|
2009-12-29T09:19:21Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137480 |
| . |
| Reference:
|
[1] Bondarenko B.A.. : Generalized Pascal Triangles and Pyramids: Their Fractals., Graphs, and Applications, pp. 36-37. Santa Clara, CA: The Fibonacci Association, 1993. Zbl 0792.05001 |
| Reference:
|
[2] Ericksen L. : “Golden Tuple Products.”.To Appear In Applications of Fibonacci Numbers 11, W. Webb (ed.), Dordrecht: Kluwer Academic Publishers, 2006. MR 2463524 |
| Reference:
|
[3] Foata D., Han G.-N. : “Jacobi and Watson Identities Combinatorially Revisited.”.From a Web Resource. http://cartan.u-strasbg.fr/$\sim $gnonin/paper/pub81/html. |
| Reference:
|
[4] Kang, Soon-Yi. : “A New Proof Of Winquist’s Identity.”.J. of Combin. Theory, Series A 78 (1997) 313-318. MR 1445422, 10.1006/jcta.1996.2781 |
| Reference:
|
[5] Ribenboim P.: “Primality Tests Based on Lucas Sequences.”.2.V In The Little Book of Bigger Primes, 2nd ed. New York: Springer-Verlag, p. 63, 2004. MR 2028675 |
| Reference:
|
[6] Sloane N.J.A.: Sequences $A003010$ & $A095847$.From a Web Resource. http://www.research.att.com/ njas/sequences/. |
| Reference:
|
[7] Sloane N.J.A.: $A001175$ “Pisano Number.”.From a Web Resource. http://www.research.att.com/ njas/sequences/. |
| Reference:
|
[8] Vajda S. Fibonacci & Lucas Numbers, and the Golden Section: Theory and Applications., pp. 177-178. Chichester: Ellis Horwood, 1989. MR 1015938 |
| Reference:
|
[9] Weisstein E.W. : “Delannoy Number.”.From a Web Resource. http://mathworld.wolfram.com/DelannoyNumber.html |
| Reference:
|
[10] Weisstein E.W.. : “Lucas-Lehmer Test.”.From a Web Resource. http://mathworld.wolfram.com/Lucas-LehmerTest.html |
| Reference:
|
[11] Wong C.K., Maddox T.W. : “A Generalized Pascal’s Triangle.”.The Fibonacci Quarterly 13:2 (1975) 134-136. MR 0360297 |
| . |
