A099756 For each single digit {0,1,...,9} record the smallest prime made up of copies of that digit (if there is one); repeat for all of the C(10,2) = 45 pairs of distinct decimal digits; then for all triples; etc.
11, 2, 3, 5, 7, 101, 211, 13, 41, 151, 61, 17, 181, 19, 23, 227, 29, 43, 53, 37, 83, 47, 449, 557, 59, 67, 787, 79, 89, 1021, 103, 401, 1051, 601, 107, 1801, 109, 2003, 2027, 2029, 4003, 503, 307, 3083, 4007, 409, 5077, 509, 607, 8087, 709, 809, 1123, 241, 251, 1621
Offset: 1
Examples
There are no primes that consist of copies of the digit 4, or 6, or 8, or 9, or {0,2}, or {0,3}, ..., {0,2,4,5,6,8}.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..950
Programs
-
Mathematica
ss = Subsets[Range[0, 9], 10]; dlt = {1, 2, 6, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 30, 31, 32, 34, 38, 41, 42, 43, 45, 47, 49, 52, 53, 66, 67, 68, 70, 74, 77, 78, 79, 81, 83, 85, 88, 89, 127, 128, 130, 132, 134, 137, 153, 157, 159, 162, 168, 211, 212, 214, 216, 218, 221, 237, 241, 243, 246, 252, 332, 334, 337, 343, 373, 458, 460, 463, 469, 499, 604, 730}; ss = Delete[ss, {#} & /@ dlt]; k = 1; lst = {}; f[n_] := Block[{id = ss[[n]], p = NextPrime[ NestWhileList[ Quotient[#, 10] &, FromDigits[ss[[n]]], # > 0 &][[-2]]*10^(Length[ ss[[n]]] - If[ Mod[ FromDigits@ ss[[n]], 3] == 0, 0, 1]) - 1]}, While[ Union@ IntegerDigits@ p != id, p = NextPrime@ p]; p]; f[3] = 3; Array[ f, 950] (* Robert G. Wilson v, Apr 06 2024 *)
Extensions
More terms from Labos Elemer, Nov 15 2004