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Numbers of the form i*5^j-1 (i=1..4, j >= 0).
10

%I #30 May 05 2024 03:30:23

%S 0,1,2,3,4,9,14,19,24,49,74,99,124,249,374,499,624,1249,1874,2499,

%T 3124,6249,9374,12499,15624,31249,46874,62499,78124,156249,234374,

%U 312499,390624,781249,1171874,1562499,1953124,3906249,5859374,7812499,9765624,19531249,29296874,39062499,48828124,97656249,146484374,195312499

%N Numbers of the form i*5^j-1 (i=1..4, j >= 0).

%C Row numbers of Pascal's Triangle where none of the binomial coefficients in that row is divisible by 5. - _Thomas M. Green_, Apr 02 2013

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,5,-5).

%F a(n) = a(n-1)+5*a(n-4)-5*a(n-5). G.f.: x^2*(x+1)*(x^2+1) / ((x-1)*(5*x^4-1)). [_Colin Barker_, Feb 01 2013]

%e For n = 7, a(7) = 14 and the binomial coefficients in the 14th row of Pascal's Triangle are 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1 and none of the elements in that row is divisible by 5. - _Thomas M. Green_, Apr 05 2013

%Y Smallest number whose base b sum of digits is n: A000225 (b=2), A062318 (b=3), A180516 (b=4), this sequence (b=5), A181288 (b=6), A181303 (b=7), A165804 (b=8), A140576 (b=9), A051885 (b=10). - _Jason Kimberley_, Nov 02 2011

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Jan 25 2011