A378553 - OEIS

%I #21 Dec 01 2024 10:06:22

%S 4,61,551,4026,24687,125841,510370,1542450,3120693,3265920

%N The number of n-digit composite numbers with all digits distinct.

%C This sequence is finite since there are no numbers at all which have 11 or more distinct decimal digits.

%C For n=10, the sum of 10 distinct digits is 0+1+..+9 = 45 which by "casting out 9s" shows such a number is divisible by 9 and so always composite.

%F a(n) <= A073531(n) with equality only for n = 10.

%e a(2) = 61 because there are 61 two-digit composite numbers with distinct digits: 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 26, 27, 28, 30, 32, 34, 35, 36, 38, 39, 40, 42, 45, 46, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 98.

%Y Cf. A073531, A210441, A073532.

%K nonn,base,fini,full

%O 1,1

%A _Shyam Sunder Gupta_, Nov 30 2024