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%I #11 Dec 03 2019 21:13:30
%S 12,15,21,33,60,75,84,93,123,186,264,327,384,519,651,654,678,726,753,
%T 762,771,807,831,852,870,897,924,975,993,1023,1029,1056,1110,1122,
%U 1128,1149,1194,1203,1248,1257,1272,1290,1302,1308,1317,1347,1407,1437,1443,1464,1482,1524,1527,1533,1554,1581,1644,1662,1677
%N Numbers n such that digital root of n is 3*(digital root of n-th prime).
%C Corresponding primes:
%C 37, 47, 73, 137, 281, 379, 433, 487, 677, 1109, 1693, 2179, 2657, 3719, 4861, 4889, 5077, 5501, 5717, 5807, 5861, 6203, 6373, 6581, 6761, 6977, 7229, 7687, 7867, 8147, 8209, 8443, 8929, 9029, 9091, 9281, 9677, 9749, 10163, 10253, 10369, 10567, 10667, 10729, 10837, 11117, 11719, 11981.
%C Conjecture: a(n) ~ 27n. - _Charles R Greathouse IV_, Jun 18 2015
%C All terms are divisible by 3 but not by 9. - _Robert Israel_, Dec 03 2019
%H Robert Israel, <a href="/A259040/b259040.txt">Table of n, a(n) for n = 1..10000</a>
%p droot:= n -> subs(0=9, n mod 9):
%p select(t -> droot(t) = 3*droot(ithprime(t)), [seq(i,i=3..10000,3)]); # _Robert Israel_, Dec 03 2019
%t Reap[Do[If[FixedPoint[Total[IntegerDigits[#]]&,n]==3*Mod[Prime[n], 9], Sow[{n,Prime[n]}]],{n,2000}]][[2,1]]
%o (PARI) n=0; forprime(p=2, 1e4, if(p%9*3==n++%9, print1(n", "))) \\ _Charles R Greathouse IV_, Jun 18 2015
%Y Cf. A010888, A038194, A258876, A258877, A259032.
%K nonn,base
%O 1,1
%A _Zak Seidov_, Jun 17 2015
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