cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A258877 Primes p=prime(m) such that both p and m have the same digital root.

Original entry on oeis.org

97, 131, 199, 263, 349, 457, 479, 521, 541, 617, 661, 733, 829, 839, 881, 1039, 1049, 1091, 1103, 1277, 1289, 1301, 1361, 1433, 1487, 1499, 1549, 1571, 1759, 1913, 1933, 1993, 2089, 2099, 2129, 2141, 2221, 2273, 2357, 2377, 2389, 2441
Offset: 1

Views

Author

Zak Seidov, Jun 13 2015

Keywords

Examples

			Both 97 = prime(25) and 25 have digital root = 7,
both 131 = prime(32) and 32 have digital root = 5.

Crossrefs

Cf. A000040, A010888, A038194, A258876.

Programs

  • Mathematica
    Reap[Do[If[FixedPoint[Total[IntegerDigits[#]]&,n]==Mod[(p=Prime[n]),9],Sow[p]],{n,439}]][[2,1]]
Prime[Select[Range@370,Mod[#,9]==Mod[Prime[#],9]&]] (* Ivan N. Ianakiev, Jun 18 2015 *)

Formula

a(n) = A000040(A258876(n)).

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

Original entry on oeis.org

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

Views

Author

Zak Seidov, Jun 17 2015

Keywords

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

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

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

Original entry on oeis.org

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

Views

Author

Zak Seidov, Jun 17 2015

Keywords

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

A259028 a(n) = least number m such that digital root of m is n*(digital root of m-th prime).

Original entry on oeis.org

25, 29, 12, 26, 131, 42, 106, 8, 63
Offset: 1

Views

Author

Zak Seidov, Jun 17 2015

Keywords

Comments

Corresponding pairs of m and prime(m): {25,97}, {29,109}, {12,37}, {26, 101}, {131,739}, {42,181}, {106,577}, {8,19}, {63,307}.

Crossrefs

Cf. A000040, A010888, A038194, A258876, A258877.

Programs

  • Mathematica
    Table[m = 1; While[FixedPoint[Total@ IntegerDigits[#] &, m] != n FixedPoint[Total@ IntegerDigits[#] &, Prime@ m], m++]; m, {n, 9}] (* Michael De Vlieger, Jun 19 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

Views

Author

Zak Seidov, Jun 17 2015

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    Reap[Do[If[FixedPoint[Total[IntegerDigits[#]]&,n]==4*Mod[Prime[n],9], Sow[{n,Prime[n]}]],{n,2000}]][[2,1]]
  • PARI
    n=0; forprime(p=2, 1e4, if(p%9*4==n++%9, print1(n", "))) \\ Charles R Greathouse IV, Jun 18 2015
Showing 1-5 of 5 results.

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