login
Triangular numbers that are also brilliant (A078972).
3

%I #10 Nov 21 2013 12:48:46

%S 6,10,15,21,253,703,1081,1711,1891,2701,3403,25651,34453,38503,49141,

%T 60031,64261,73153,79003,88831,104653,108811,114481,126253,146611,

%U 158203,171991,188191,218791,226801,258121,269011,286903,351541,371953,385003,392941

%N Triangular numbers that are also brilliant (A078972).

%C Smallest value where each factor has n digits for n = 1, 2, 3, 4, 5, are: 6 = 2 * 3; 253 = 11 * 23; 25651 = 113 * 227; 2035153 = 1009 * 2017; 202457503 = 10061 * 20123. [From _Jonathan Vos Post_, Apr 04 2009]

%H Donovan Johnson, <a href="/A113940/b113940.txt">Table of n, a(n) for n = 1..1000</a>

%F A000217 INTERSECTION A078972. Subset of A068443. [From _Jonathan Vos Post_, Apr 04 2009]

%e 253 = T(22) and 253 = 11*23 is brilliant.

%t brilQ[n_]:=Module[{fin=FactorInteger[n]},Total[Transpose[fin][[2]]]==2&& Length[Union[IntegerLength[Transpose[fin][[1]]]]]==1]

%t Intersection[Accumulate[Range[850]],Select[Range[362000],brilQ]] (* _Harvey P. Dale_, Feb 06 2011 *)

%Y Cf. A068443, A078972, A000217.

%K base,nonn

%O 1,1

%A _Giovanni Resta_, Jan 31 2006