A048865 -id:A048865 - cp's OEIS frontend

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

Dmitrii Ubskii, Feb 17 2017

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).

			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.

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

Cf. A000720, A001221, A048865.

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 *)

A048982 Number of numbers which have a "prime-rich" reduced residue system (RRS) and binary order n.

Original entry on oeis.org

0, 0, 0, 1, 3, 8, 15, 22, 32, 50, 85, 80, 98, 84, 59, 37, 10, 2, 0, 0, 0

Offset: 0

Labos Elemer

It is remarkable that in exponentially increasing ranges these occurrences increase to n=13 and thereafter decline to zero. So A048868 is believed to be finite.

			In binary order (A029837) zone of 7, i.e., in [65,128], 22 numbers belong to A048868: 66, 68, 70, 72, 74, 76, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 108, 110, 112, 114, 120, and 126. The largest term is 90090. The largest 4 are divisible by 2310, the largest 28 by 210, and the largest 103 by 30.

Cf. A048862, A048863, A048864, A048865, A048866, A048867, A048868, A048869.

Cf. A002110, A029837, A048597.

cp's OEIS Frontend

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

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