cp's OEIS Frontend

A154523 Numbers k such that the smallest decimal digit of k equals the smallest decimal digit of prime(k).

%I A154523 #15 Feb 11 2019 21:54:36
%S A154523 11,13,18,31,41,52,62,73,80,81,110,112,113,114,115,116,121,125,128,
%T A154523 133,135,140,141,142,152,156,157,164,167,170,180,187,188,189,191,192,
%U A154523 193,194,195,196,198,199,211,215,216,217,218,219,221,231,241,251,261,271
%N A154523 Numbers k such that the smallest decimal digit of k equals the smallest decimal digit of prime(k).
%C A154523 Natural density 1, since almost all numbers and almost all primes (thanks to the prime number theorem) contain the digit 0.
%C A154523 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 A154523 Harvey P. Dale, <a href="/A154523/b154523.txt">Table of n, a(n) for n = 1..1000</a>
%e A154523 11 is a term because prime(11) =  31 (smallest digits: 1);
%e A154523 13 is a term because prime(13) =  41 (smallest digits: 1);
%e A154523 18 is a term because prime(18) =  61 (smallest digits: 1);
%e A154523 31 is a term because prime(31) = 127 (smallest digits: 1);
%e A154523 41 is a term because prime(41) = 179 (smallest digits: 1);
%e A154523 52 is a term because prime(52) = 239 (smallest digits: 2).
%p A154523 A054054 := proc(n) min(op(convert(n,base,10)) ) ; end proc:
%p A154523 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 A154523 Transpose[Select[Table[{n,Prime[n]},{n,300}],Min[IntegerDigits[#[[1]]]] == Min[IntegerDigits[#[[2]]]]&]][[1]] (* _Harvey P. Dale_, Dec 18 2012 *)
%Y A154523 Cf. A020472, A106110.
%K A154523 nonn,base,less
%O A154523 1,1
%A A154523 _Juri-Stepan Gerasimov_, Jan 11 2009
%E A154523 Corrected (221 inserted) by _R. J. Mathar_, May 05 2010
%E A154523 Definition clarified by _Harvey P. Dale_, Dec 18 2012