Iterated digit sums, recursions and primality

Larry Ericksen

Acta Mathematica Universitatis Ostraviensis (2006)

  • Volume: 14, Issue: 1, page 27-35
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Ericksen, Larry. "Iterated digit sums, recursions and primality." Acta Mathematica Universitatis Ostraviensis 14.1 (2006): 27-35. <http://eudml.org/doc/35159>.

@article{Ericksen2006,
abstract = {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.},
author = {Ericksen, Larry},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {sum of digits; recursive sequences; triple product identity; quintuple product; primality testing; digit sums; Lucas-Lehmer numbers},
language = {eng},
number = {1},
pages = {27-35},
publisher = {University of Ostrava},
title = {Iterated digit sums, recursions and primality},
url = {http://eudml.org/doc/35159},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Ericksen, Larry
TI - Iterated digit sums, recursions and primality
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2006
PB - University of Ostrava
VL - 14
IS - 1
SP - 27
EP - 35
AB - 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.
LA - eng
KW - sum of digits; recursive sequences; triple product identity; quintuple product; primality testing; digit sums; Lucas-Lehmer numbers
UR - http://eudml.org/doc/35159
ER -

References

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  2. Ericksen L., “Golden Tuple Products.”, To Appear In Applications of Fibonacci Numbers 11, W. Webb (ed.), Dordrecht: Kluwer Academic Publishers, 2006. MR2463524
  3. Foata D., Han G.-N., “Jacobi and Watson Identities Combinatorially Revisited.”, From a Web Resource. http://cartan.u-strasbg.fr/gnonin/paper/pub81/html. 
  4. Kang, Soon-Yi., 10.1006/jcta.1996.2781, J. of Combin. Theory, Series A 78 (1997) 313-318. (1997) MR1445422DOI10.1006/jcta.1996.2781
  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. MR2028675
  6. Sloane N.J.A., Sequences A 003010 A 095847 , From a Web Resource. http://www.research.att.com/ njas/sequences/. 
  7. Sloane N.J.A., A 001175 “Pisano Number.”, From a Web Resource. http://www.research.att.com/ njas/sequences/. 
  8. Vajda S. Fibonacci & Lucas Numbers, and the Golden Section, Theory and Applications, , pp. 177-178. Chichester: Ellis Horwood, 1989. (1989) MR1015938
  9. Weisstein E.W., “Delannoy Number.”, From a Web Resource. http://mathworld.wolfram.com/DelannoyNumber.html 
  10. Weisstein E.W.., “Lucas-Lehmer Test.”, From a Web Resource. http://mathworld.wolfram.com/Lucas-LehmerTest.html 
  11. Wong C.K., Maddox T.W., “A Generalized Pascal’s Triangle.”, The Fibonacci Quarterly 13:2 (1975) 134-136. (1975) MR0360297

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