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A109133
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Numbers k such that (sum of digits)*(number of digits) + 1 is prime.
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1
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1, 2, 4, 6, 10, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 41, 42, 44, 45, 47, 50, 51, 53, 54, 56, 59, 60, 62, 63, 65, 68, 69, 71, 72, 74, 77, 78, 80, 81, 83, 86, 87, 90, 92, 95, 96, 99, 101, 103, 105, 109, 110, 112, 114, 118, 121, 123, 127
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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By Dirichlet's theorem on primes in arithmetic progressions, for any positive integer k this sequence has infinitely many terms of the form k*10^m. - Robert Israel, Dec 19 2021
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LINKS
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EXAMPLE
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1234 is a term because 4*(1+2+3+4)+1 = 41.
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MAPLE
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filter:= proc(n) local L;
L:= convert(n, base, 10);
isprime(convert(L, `+`)*nops(L)+1)
end proc:
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MATHEMATICA
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Select[Range[130], PrimeQ[Total[IntegerDigits[#]]IntegerLength[ #]+ 1]&] (* Harvey P. Dale, Jul 12 2011 *)
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PROG
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(Python)
from sympy import isprime
def ok(n): s = str(n); return isprime(sum(map(int, s))*len(s) + 1)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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