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%I #11 Jun 20 2015 14:47:49
%S 29,38,40,44,49,80,143,148,166,191,197,233,251,269,272,283,305,314,
%T 326,335,364,371,373,389,425,427,431,461,470,497,515,517,553,557,562,
%U 602,614,616,625,634,638,647,652,656,659,661,677,683,692,731,749,758,800,812,845,863,908
%N Numbers n such that digital root of n is 2*(digital root of n-th prime).
%C Corresponding primes:
%C 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.
%C Conjecture: a(n) ~ 18n. - _Charles R Greathouse IV_, Jun 18 2015
%t Reap[Do[If[FixedPoint[Total[IntegerDigits[#]]&,n]==2*Mod[Prime[n],9],Sow[n]], {n,1000}]][[2,1]]
%t Select[Range@ 1000, FixedPoint[Total@ IntegerDigits@ # &, #] == 2 FixedPoint[Total@ IntegerDigits@ # &, Prime@ #] &] (* _Michael De Vlieger_, Jun 19 2015 *)
%o (PARI) n=0;forprime(p=2,1e4, if(p%9*2==n++%9, print1(n", "))) \\ _Charles R Greathouse IV_, Jun 18 2015
%Y Cf. A010888, A038194, A258876, A258877, A259040.
%K nonn,base
%O 1,1
%A _Zak Seidov_, Jun 17 2015
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