A373645 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).

2, 11, 114, 894, 13155, 127041, 2219826, 44489860, 1023485967, 26436195405, 755182183459, 23609378957430, 802775563829902, 29480898988179429, 1162849454580682365

Offset: 2

Author

Scott R. Shannon, Jun 12 2024

Keywords

• nonn
• base
• more

Comments

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

Examples

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

Crossrefs

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

Cf. A374225.