A259032 -id:A259032 - cp's OEIS frontend

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

Zak Seidov, Jun 17 2015

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

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

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

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

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

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

A259041 Numbers n such that digital root of n is 4*(digital root of n-th prime).

Original entry on oeis.org

26, 31, 58, 71, 89, 107, 112, 116, 157, 161, 193, 211, 247, 310, 337, 395, 458, 490, 503, 535, 580, 584, 620, 688, 769, 778, 841, 850, 859, 868, 872, 877, 895, 949, 985, 989, 1034, 1070, 1079, 1102, 1106, 1133, 1138, 1142, 1192, 1201, 1210, 1214, 1219, 1232, 1255, 1277, 1282, 1295, 1300, 1327, 1412, 1493, 1511, 1538

Offset: 1

Zak Seidov, Jun 17 2015

Corresponding primes:
101, 127, 271, 353, 461, 587, 613, 641, 919, 947, 1171, 1297, 1567, 2053, 2269, 2711, 3251, 3511, 3593, 3853, 4231, 4259, 4583, 5167, 5851, 5923, 6481, 6571, 6661, 6733, 6779, 6823, 6967, 7489, 7759, 7823, 8237, 8597, 8669, 8839, 8867, 9137, 9181, 9209, 9649, 9739, 9811, 9839, 9883.
Conjecture: a(n) ~ 27n. - Charles R Greathouse IV, Jun 18 2015

Cf. A010888, A038194, A258876, A258877, A259032, A259040.

Reap[Do[If[FixedPoint[Total[IntegerDigits[#]]&,n]==4*Mod[Prime[n],9], Sow[{n,Prime[n]}]],{n,2000}]][[2,1]]

n=0; forprime(p=2, 1e4, if(p%9*4==n++%9, print1(n", "))) \\ Charles R Greathouse IV, Jun 18 2015

cp's OEIS Frontend

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

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