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

1,2

References

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

Links

Table of n, a(n) for n=1..36.

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A092301 A229668 A165343 * A361072 A266639 A203496

Adjacent sequences: A278313 A278314 A278315 * A278317 A278318 A278319

Keyword

nonn,base

Author

Volker Diels-Grabsch, Nov 18 2016

Extensions

More terms from Jon E. Schoenfield, Dec 02 2016

Status

approved