OFFSET
1,1
COMMENTS
Natural density 1, since almost all numbers and almost all primes (thanks to the prime number theorem) contain the digit 0.
The first terms with smallest digit 1, 2, and 3 are listed in the Data section. The first with smallest digits 4, 5, and 6 are 644, 758, and 6666, respectively. While there are plenty of primes with no decimal digit smaller than 7 (see A106110), including many primes consisting only of the digits 8 and 9 (the 10th of which is prime(77777) = 989999; cf. A020472), it seems to me that finding a term in this sequence whose smallest digit is 7 or 8 should be a very difficult problem. - Jon E. Schoenfield, Feb 11 2019
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
11 is a term because prime(11) = 31 (smallest digits: 1);
13 is a term because prime(13) = 41 (smallest digits: 1);
18 is a term because prime(18) = 61 (smallest digits: 1);
31 is a term because prime(31) = 127 (smallest digits: 1);
41 is a term because prime(41) = 179 (smallest digits: 1);
52 is a term because prime(52) = 239 (smallest digits: 2).
MAPLE
A054054 := proc(n) min(op(convert(n, base, 10)) ) ; end proc:
for n from 1 to 500 do if A054054(n) = A054054(ithprime(n)) then printf("%d, ", n ) ; end if; end do: (End) # R. J. Mathar, May 05 2010
MATHEMATICA
Transpose[Select[Table[{n, Prime[n]}, {n, 300}], Min[IntegerDigits[#[[1]]]] == Min[IntegerDigits[#[[2]]]]&]][[1]] (* Harvey P. Dale, Dec 18 2012 *)
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
Juri-Stepan Gerasimov, Jan 11 2009
EXTENSIONS
Corrected (221 inserted) by R. J. Mathar, May 05 2010
Definition clarified by Harvey P. Dale, Dec 18 2012
STATUS
approved