A300186 Largest digit sum among all n-digit primes.

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

Offset

1,1

Comments

Largest value of A007605(x) for any integer x in the interval [A090226(n), A090226(n+1)-1].

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.

Links

Table of n, a(n) for n=1..55.

Example

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.

Prog

(PARI) a(n) = my(r=0); forprime(p=10^(n-1), 10^n, if(sumdigits(p) > r, r=sumdigits(p))); r

Crossrefs

Cf. A007605, A008591, A017257, A055642, A090226, A263431.

Sequence in context: A072199 A309231 A183897 * A355680 A354672 A261934

Adjacent sequences: A300183 A300184 A300185 * A300187 A300188 A300189

Keyword

nonn,base

Author

Felix Fröhlich, Feb 28 2018

Extensions

More terms from Alois P. Heinz, Feb 28 2018

Status

approved