A259032 Numbers n such that digital root of n is 2*(digital root of n-th prime).

29, 38, 40, 44, 49, 80, 143, 148, 166, 191, 197, 233, 251, 269, 272, 283, 305, 314, 326, 335, 364, 371, 373, 389, 425, 427, 431, 461, 470, 497, 515, 517, 553, 557, 562, 602, 614, 616, 625, 634, 638, 647, 652, 656, 659, 661, 677, 683, 692, 731, 749, 758, 800, 812, 845, 863, 908

Offset: 1

Author

Zak Seidov, Jun 17 2015

Keywords

• nonn
• base

Comments

Corresponding primes:

109, 163, 173, 193, 227, 409, 823, 857, 983, 1153, 1201, 1471, 1597, 1723, 1747, 1847, 2011, 2083, 2161, 2251, 2459, 2539, 2549, 2683, 2953, 2963, 3001, 3259, 3331, 3547, 3691, 3701, 4007, 4027, 4079, 4423, 4519, 4547, 4637, 4691, 4729, 4801, 4871, 4909, 4933, 4943, 5059, 5107, 5197.

Conjecture: a(n) ~ 18n. - Charles R Greathouse IV, Jun 18 2015

Crossrefs

Cf. A010888, A038194, A258876, A258877, A259040.

Programs

Mathematica

Reap[Do[If[FixedPoint[Total[IntegerDigits[#]]&,n]==2*Mod[Prime[n],9],Sow[n]], {n,1000}]][[2,1]]
Select[Range@ 1000, FixedPoint[Total@ IntegerDigits@ # &, #] == 2 FixedPoint[Total@ IntegerDigits@ # &, Prime@ #] &] (* Michael De Vlieger, Jun 19 2015 *)

PARI

n=0;forprime(p=2,1e4, if(p%9*2==n++%9, print1(n", "))) \\ Charles R Greathouse IV, Jun 18 2015