A282509 a(n) is the largest number such that every subsequence of digits of the number written in base n is prime.

2, 11, 17, 23, 37, 491, 47, 73, 79, 6043, 67, 193, 197, 211, 223, 5639, 211, 4783, 401, 3467, 439, 41357, 577, 617, 461, 18133, 379, 60899, 157, 17827, 761, 3847, 1087, 38201, 853, 45641, 743, 59723, 113, 246173, 1249, 14831, 1847, 49177, 1741, 109141, 2011, 104053, 2399, 128599, 2281, 157127, 2917, 11149, 3023, 43913, 2539

Offset: 3

Author

Dmitrii Ubskii, Feb 17 2017

Keywords

• nonn
• base

Comments

For odd n the number will have the form p2, 2p, or p, where p is a prime digit in base n.

For even n the number of digits cannot exceed pi(n)-omega(n)+1 = A048865(n)+1, where pi(n) is the number of primes <= n (A000720), omega(n) is number of distinct primes dividing n (A001221).

Examples

			In base-12 35B7 (6043 in base-10) is prime, and all of 35B, 357, 3B7, 5B7, 35, 3B, 37, 5B, 57, B7, 3, 5, B, and 7 are prime.
		

Links

• Dmitrii Ubskii, Table of n, a(n) for n = 3..500

Crossrefs

Cf. A000720, A001221, A048865.

Programs

Mathematica

a[b_] := Block[{m,p,r}, p = Select[Range[b-1], PrimeQ]; m = 0; r[n_] := Block[{}, m = Max[m, n]; r /@ Select[n*b+p, PrimeQ[#] && And @@ PrimeQ /@ (FromDigits[#, b] & /@ Subsets[IntegerDigits[#, b], {2, Infinity}]) &];]; r@0; m]; a /@ Range[3, 100] (* Giovanni Resta, Feb 21 2017 *)