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

1, 3, 661, 983, 2631, 2893, 12385, 12893, 14661, 18615, 27519, 35383, 36213, 38691, 46215, 49231, 83631, 87291, 92843, 113865, 116683, 123415, 129815, 136423, 139261, 152619, 161683, 162435, 166817, 178119, 194725, 244635, 247941, 254663, 274165, 276941

Offset: 1

Author

Volker Diels-Grabsch, Nov 18 2016

Keywords

• nonn
• base

Examples

			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).
		

References

• Michael Huke, Solution to exercise psi-15 (German language article), WURZEL 11/2016, November 2016, page 252, http://wurzel.org/

Crossrefs

Odd terms of A256115. - Michel Marcus, Dec 04 2016

Programs

Mathematica

Select[Range[1, 10^6, 2], And[MatchQ @@ #, Times @@ # != 0] &@{(Times @@ IntegerDigits@ #)^2, Times @@ IntegerDigits[#^2]} &] (* Michael De Vlieger, Dec 06 2016 *)

PARI

pd(n) = my(d=digits(n)); prod(k=1, #d, d[k]);
isok(n) = (n % 2) && (p = pd(n)^2) && (p == pd(n^2)); \\ Michel Marcus, Dec 04 2016

Extensions

More terms from Jon E. Schoenfield, Dec 02 2016