A259040 Numbers n such that digital root of n is 3*(digital root of n-th prime).

12, 15, 21, 33, 60, 75, 84, 93, 123, 186, 264, 327, 384, 519, 651, 654, 678, 726, 753, 762, 771, 807, 831, 852, 870, 897, 924, 975, 993, 1023, 1029, 1056, 1110, 1122, 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

Offset: 1

Author

Zak Seidov, Jun 17 2015

Keywords

• nonn
• base

Comments

Corresponding primes:

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.

Conjecture: a(n) ~ 27n. - Charles R Greathouse IV, Jun 18 2015

All terms are divisible by 3 but not by 9. - Robert Israel, Dec 03 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010888, A038194, A258876, A258877, A259032.

Programs

Maple

droot:= n -> subs(0=9, n mod 9):
select(t -> droot(t) = 3*droot(ithprime(t)), [seq(i,i=3..10000,3)]); # Robert Israel, Dec 03 2019

Mathematica

Reap[Do[If[FixedPoint[Total[IntegerDigits[#]]&,n]==3*Mod[Prime[n], 9], Sow[{n,Prime[n]}]],{n,2000}]][[2,1]]

PARI

n=0; forprime(p=2, 1e4, if(p%9*3==n++%9, print1(n", "))) \\ Charles R Greathouse IV, Jun 18 2015