|
%I #13 Feb 12 2021 11:50:45
%S 0,1,6,231,780,1770,2850,3003,4560,14028,17205,20301,20706,24090,
%T 24531,28203,32640,37401,43071,80601,96580,102831,103740,112101,
%U 191890,200661,201930,239086,255970,286903,296065,302253,303810,316410,318003,332520
%N Hexagonal numbers for which both the sum of the digits and the product of the digits are also hexagonal numbers.
%H David A. Corneth, <a href="/A117064/b117064.txt">Table of n, a(n) for n = 1..10000</a>
%e 24531 is in the sequence because it is a hexagonal number, the sum of its digits 2+4+5+3+1=15 is a hexagonal number and the product of its digits 2*4*5*3*1=120 is also a hexagonal number.
%t hexQ[n_] := n == 0 || IntegerQ[(Sqrt[8 n + 1] + 1)/4]; t = {0}; Do[h = n*(2 n - 1); If[hexQ[Plus @@ (z = IntegerDigits[h])] && hexQ[Times @@ z], AppendTo[t, h]], {n, 410}]; t (* _Jayanta Basu_, Jul 13 2013 *)
%o (PARI) is(n) = isHexagonal(n) && isHexagonal(sumdigits(n)) && isHexagonal(vecprod(digits(n)))
%o isHexagonal(n) = { my(c = (sqrtint(8*n + 1) + 1)>>2); c*(2*c - 1) == n } \\ _David A. Corneth_, Feb 06 2021
%Y Cf. A000384, A007953, A007954.
%K nonn,base
%O 1,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006
%E Offset corrected by _David A. Corneth_, Feb 06 2021
|
