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A300186
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Largest digit sum among all n-digit primes.
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0
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7, 17, 25, 35, 44, 53, 62, 71, 80, 88, 98, 107, 115, 125, 134, 143, 152, 161, 170, 179, 188, 197, 206, 215, 223, 233, 242, 250, 260, 269, 278, 287, 296, 304, 314, 323, 332, 341, 350, 359, 367, 377, 386, 394, 404, 413, 421, 431, 440, 449, 458, 466, 476, 485, 494
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OFFSET
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1,1
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COMMENTS
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Trivially, 1 < a(n) < 9*n = A008591(n). The lower bound follows, since a prime > 10 must contain at least two nonzero digits, with the least possible digit sum 2. The upper bound follows because 10^n-1 is always composite and thus the digit sum can be at most A017257(n-1). The maximal possible value is reached by a(n) iff a term t exists in A263431 such that A055642(t) = n-1.
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LINKS
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EXAMPLE
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For n = 2: Among all 2-digit primes, the largest possible digit sum is 8+9 = 17, which is achieved by the prime 89, so a(2) = 17.
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PROG
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(PARI) a(n) = my(r=0); forprime(p=10^(n-1), 10^n, if(sumdigits(p) > r, r=sumdigits(p))); r
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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