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

Author

Felix Fröhlich, Feb 28 2018

Keywords

• nonn
• base

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.

Examples

			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.
		

Crossrefs

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

Programs

PARI

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

Extensions

More terms from Alois P. Heinz, Feb 28 2018