Search: id:A055272 Results 1-1 of 1 results found. %I A055272 %S A055272 1,6,42,294,2058,14406,100842,705894,4941258,34588806,242121642, %T A055272 1694851494,11863960458,83047723206,581334062442,4069338437094, %U A055272 28485369059658,199397583417606,1395783083923242,9770481587462694 %N A055272 First differences of 7^n (A000420). %C A055272 Partial sum of A055270. %C A055272 Conjecture in "Introduction a la theorie des nombres" by d'Armel Mercier and J. M. Deconinck: this is the period length of the fraction 1/ 7^n. For example 1/7^2=0.0204081632653061224489795918367346938775510204....with a period of 42 digits =6*7=a(2). The period of 1/7^3 has exactly 294=a(3) digits. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2002 %C A055272 Also phi(7^n), where phi is Euler's totient function. - Alonso Delarte (alonso.delarte(AT)gmail.com), May 08 2006 %C A055272 For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2, 3,4,5,6,7} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6,7} we have f(x)<>y. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Mar 27 2007 %D A055272 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196. %H A055272 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets %F A055272 a(n)=6*7^(n-1), a(0)=1. %e A055272 a(n)=7a(n-1)+[(-1)^n]*C(1,1-n). G.f.(x)=(1-x)/(1-7x). %t A055272 Table[EulerPhi[7^n], {n, 0, 19}] - Alonso Delarte (alonso.delarte(AT)gmail.com), May 08 2006 %Y A055272 Cf. A000420 and A055270. %Y A055272 Sequence in context: A057089 A110711 A156361 this_sequence A155196 A147838 A127628 %Y A055272 Adjacent sequences: A055269 A055270 A055271 this_sequence A055273 A055274 A055275 %K A055272 easy,nonn %O A055272 0,2 %A A055272 Barry E. Williams, May 28 2000 %E A055272 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 30 2000 Search completed in 0.001 seconds