%I #15 Feb 11 2019 21:54:36

%S 11,13,18,31,41,52,62,73,80,81,110,112,113,114,115,116,121,125,128,

%T 133,135,140,141,142,152,156,157,164,167,170,180,187,188,189,191,192,

%U 193,194,195,196,198,199,211,215,216,217,218,219,221,231,241,251,261,271

%N Numbers k such that the smallest decimal digit of k equals the smallest decimal digit of prime(k).

%C Natural density 1, since almost all numbers and almost all primes (thanks to the prime number theorem) contain the digit 0.

%C 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

%H Harvey P. Dale, <a href="/A154523/b154523.txt">Table of n, a(n) for n = 1..1000</a>

%e 11 is a term because prime(11) = 31 (smallest digits: 1);

%e 13 is a term because prime(13) = 41 (smallest digits: 1);

%e 18 is a term because prime(18) = 61 (smallest digits: 1);

%e 31 is a term because prime(31) = 127 (smallest digits: 1);

%e 41 is a term because prime(41) = 179 (smallest digits: 1);

%e 52 is a term because prime(52) = 239 (smallest digits: 2).

%p A054054 := proc(n) min(op(convert(n,base,10)) ) ; end proc:

%p 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

%t Transpose[Select[Table[{n,Prime[n]},{n,300}],Min[IntegerDigits[#[[1]]]] == Min[IntegerDigits[#[[2]]]]&]][[1]] (* _Harvey P. Dale_, Dec 18 2012 *)

%Y Cf. A020472, A106110.

%K nonn,base,less

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 11 2009

%E Corrected (221 inserted) by _R. J. Mathar_, May 05 2010

%E Definition clarified by _Harvey P. Dale_, Dec 18 2012