A373645 - OEIS

%I #10 Jun 18 2024 08:20:20

%S 2,11,114,894,13155,127041,2219826,44489860,1023485967,26436195405,

%T 755182183459,23609378957430,802775563829902,29480898988179429,

%U 1162849454580682365

%N The smallest number whose prime factor concatenation, as well as the number itself, when written in base n, contains all digits 0,1,...,(n-1).

%C For base 2 and base 3 the number is prime; are there other bases where this is also true?

%e a(5) = 894 = 12034_5 which contains all the digits 0..4, and 894 = 2 * 3 * 149 = 2_5 * 3_5 * 1044_5, and the factors contain all digits 0..4.

%e a(10) = 1023485967 which contains all digits 0..9, and 1023485967 = 3 * 3 * 7 * 16245809, and the factors contain all digits 0..9.

%e a(15) = 29480898988179429 = 102345C86EA7BD9_15 which contains all the digits 0..E, and 29480898988179429 = 3 * 7 * 17 * 139 * 594097474723 = 3_15 * 7_15 * 12_15 * 94_15 * 106C1A8B5ED_15, and the factors contain all digits 0..E.

%Y Cf. A372309, A358003, A372384, A372280, A372295, A372249, A027746.

%K nonn,base,more

%O 2,1

%A _Scott R. Shannon_, Jun 12 2024