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A154523
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Numbers k such that the smallest decimal digit of k equals the smallest decimal digit of prime(k).
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1
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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
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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).
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MAPLE
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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
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MATHEMATICA
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Transpose[Select[Table[{n, Prime[n]}, {n, 300}], Min[IntegerDigits[#[[1]]]] == Min[IntegerDigits[#[[2]]]]&]][[1]] (* Harvey P. Dale, Dec 18 2012 *)
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CROSSREFS
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KEYWORD
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nonn,base,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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