A258876 Integers k such that both k and prime(k) have the same digital root.

25, 32, 46, 56, 70, 88, 92, 98, 100, 113, 121, 130, 145, 146, 152, 175, 176, 182, 185, 206, 209, 212, 218, 227, 236, 239, 244, 248, 274, 293, 295, 301, 316, 317, 320, 323, 331, 338, 350, 352, 355, 362, 377, 386, 394, 397, 398, 406, 409, 413, 439

Offset: 1

Author

Zak Seidov, Jun 13 2015

Keywords

• base
• nonn

Comments

Integers k such that A010888(k) = A038194(k).

Conjecture: a(n) ~ 9n. - Charles R Greathouse IV, Jun 17 2015

Examples

			Both 25 and prime(25) = 97 have 7 for a digital root.
Both 32 and prime(32) = 131 have 5 for a digital root.
		

Links

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

Crossrefs

Cf. A010888, A038194.

Programs

Mathematica

Reap[Do[If[FixedPoint[Total[IntegerDigits[#]] &, n] == Mod[Prime[n], 9], Sow[n]], {n, 439}]][[2, 1]] (* Seidov *)
Select[Range[500], Mod[#, 9] == Mod[Prime[#], 9] &] (* Alonso del Arte, Jun 17 2015 *)

PARI

isok(n) = (n % 9) == (prime(n) % 9); \\ Michel Marcus, Jun 17 2015

PARI

n=0; forprime(p=2,1e4, if((p-n++)%9==0, print1(n", "))) \\ Charles R Greathouse IV, Jun 17 2015