login
Numbers n such that DENEAT(n^n) is prime, where DENEAT(n) = concatenate number of even digits in n, number of odd digits and total number of digits.
0

%I #7 Dec 15 2017 17:36:48

%S 1,2,10,12,14,26,28,34,37,44,147,156,192,229,237,246,263,282,317,325,

%T 409,413,432,436,467,510,515,534,561,570,598,600,611,636,687,702,729,

%U 738,776,818,830,859,894,901,903,914,954,1000,1014,1017,1054,1075,1080

%N Numbers n such that DENEAT(n^n) is prime, where DENEAT(n) = concatenate number of even digits in n, number of odd digits and total number of digits.

%e 12 is in the sequence because 12^12 = 8916100448256 has 9 even digits,

%e 4 odd digits and 13 total digits, yielding the prime 9413.

%t deneatQ[n_]:=Module[{idn=IntegerDigits[n^n]},PrimeQ[FromDigits[ Join[ IntegerDigits[ Count[ idn, _?EvenQ]],IntegerDigits[Count[idn,_?OddQ]], IntegerDigits[Length[idn]]]]]]; Select[Range[1200],deneatQ] (* _Harvey P. Dale_, Aug 04 2015 *)

%Y Cf. A073053.

%K base,nonn

%O 1,2

%A _Jason Earls_, Jun 03 2005