

A154523


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


1



11, 13, 18, 31, 41, 52, 62, 73, 80, 81, 110, 112, 113, 114, 115, 116, 121, 125, 128, 133, 135, 140, 141, 142, 152, 156, 157, 164, 167, 170, 180, 187, 188, 189, 191, 192, 193, 194, 195, 196, 198, 199, 211, 215, 216, 217, 218, 219, 221, 231, 241, 251, 261, 271
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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

Cf. A020472, A106110.
Sequence in context: A178339 A088561 A211457 * A107932 A143365 A090137
Adjacent sequences: A154520 A154521 A154522 * A154524 A154525 A154526


KEYWORD

nonn,base,less


AUTHOR

JuriStepan 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



