cp's OEIS Frontend

A278316 Odd numbers n such that q(n)^2 = q(n^2) != 0, where q(n) is the digit product on base 10.

%I A278316 #17 Dec 23 2016 08:05:22
%S A278316 1,3,661,983,2631,2893,12385,12893,14661,18615,27519,35383,36213,
%T A278316 38691,46215,49231,83631,87291,92843,113865,116683,123415,129815,
%U A278316 136423,139261,152619,161683,162435,166817,178119,194725,244635,247941,254663,274165,276941
%N A278316 Odd numbers n such that q(n)^2 = q(n^2) != 0, where q(n) is the digit product on base 10.
%D A278316 Michael Huke, Solution to exercise psi-15 (German language article), WURZEL 11/2016, November 2016, page 252, http://wurzel.org/
%e A278316 For n=3, a(3)=661: q(661)^2 = (6*6*1)^2 = 36^2 = 1296 = 4*3*6*9*2*1 = q(436921) = q(661^2).
%t A278316 Select[Range[1, 10^6, 2], And[MatchQ @@ #, Times @@ # != 0] &@{(Times @@ IntegerDigits@ #)^2, Times @@ IntegerDigits[#^2]} &] (* _Michael De Vlieger_, Dec 06 2016 *)
%o A278316 (PARI) pd(n) = my(d=digits(n)); prod(k=1, #d, d[k]);
%o A278316 isok(n) = (n % 2) && (p = pd(n)^2) && (p == pd(n^2)); \\ _Michel Marcus_, Dec 04 2016
%Y A278316 Odd terms of A256115. - _Michel Marcus_, Dec 04 2016
%K A278316 nonn,base
%O A278316 1,2
%A A278316 _Volker Diels-Grabsch_, Nov 18 2016
%E A278316 More terms from _Jon E. Schoenfield_, Dec 02 2016