A157678 Numbers k such that k + floor(average of digits of k) is prime.

1, 12, 16, 27, 30, 34, 38, 41, 56, 63, 67, 70, 74, 89, 92, 96, 101, 102, 105, 107, 112, 125, 128, 130, 136, 146, 147, 154, 161, 164, 168, 175, 186, 188, 190, 193, 208, 210, 219, 226, 229, 231, 236, 237, 247, 254, 258, 265, 273, 276, 278, 280, 290, 305, 308, 309

Offset: 1

Author

Kyle D. Balliet, Mar 04 2009

Keywords

• nonn
• base

Examples

			n = 89 -> 89 + floor((8+9)/2) = 89 + 8 = 97 (prime).
n = 190 -> 190 + floor((1+9+0)/3) = 190 + 3 = 193 (prime).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A172367.

Programs

Maple

a := proc (n) local nn: nn := convert(n, base, 10): if isprime(n+floor(add(nn[j], j = 1 .. nops(nn))/nops(nn))) = true then n else end if end proc: seq(a(n), n = 1 .. 350); # Emeric Deutsch, Mar 07 2009

PARI

is(n)=isprime(sumdigits(n)\#digits(n)+n) \\ Charles R Greathouse IV, Dec 27 2013

Extensions

Corrected and extended by Emeric Deutsch, Mar 07 2009