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 1-10 of 65 results. Next

A165336 Numbers that eventually reach a cycle under "x -> sum of cubes of digits of x" (see A055012).

Original entry on oeis.org

4, 13, 16, 22, 25, 28, 31, 40, 46, 49, 52, 55, 61, 64, 79, 82, 94, 97, 103, 106, 115, 127, 130, 133, 136, 151, 160, 163, 172, 199, 202, 205, 208, 217, 220, 229, 235, 238, 244, 250, 253, 256, 265, 271, 280, 283, 289, 292, 298, 301, 310, 313, 316, 325, 328, 331
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 17 2009

Keywords

Links

Crossrefs

Complement of A031179.
Subsequence of A016777; a(n) mod 3 = 1;
Union of A154820, A165337, A154877, and A165339.

A154877 Numbers that eventually reach the cycle 160-217-352 under "x -> sum of cubes of digits of x" (see A055012).

Original entry on oeis.org

16, 22, 61, 79, 97, 106, 115, 127, 151, 160, 172, 202, 217, 220, 229, 235, 238, 253, 271, 283, 292, 325, 328, 352, 382, 388, 445, 454, 457, 475, 511, 523, 532, 544, 547, 574, 601, 610, 709, 712, 721, 745, 754, 790, 823, 832, 838, 883, 907, 922, 970, 1006
Offset: 1

Views

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 16 2009

Keywords

Comments

All the numbers are of the form 3n+1.
A165330(a(n)) = 160;
Subsequence of A165336.

Examples

			Taking 79 as an example; 7^3+9^3=1072, 1^3+0^3+7^3+2^3=352, 3^3+5^3+2^3=160, 1^3+6^3+0^3=217, 2^3+1^3+7^3=352.
a(15)=229: 229 -> 2*2^3+9^3=745 -> 7^3+4^3+5^3+1=532 -> 5^3+3^3+2^3=160 -> 217 -> 352 -> 160 ... .

Crossrefs

Cf. A154820, A154877, A165330, A165336, A165337, A165339.

Programs

  • Mathematica
    okQ[n_]:=MemberQ[NestList[Total[IntegerDigits[#]^3]&,n,20],160]; Select[Range[1200],okQ] (* Harvey P. Dale, Jun 20 2011 *)

Extensions

Further terms added by Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 20 2009
Corrected by Reinhard Zumkeller, Sep 17 2009.
Confirmed by Harvey P. Dale, Jun 20 2011
Entry revised by N. J. A. Sloane, Oct 13 2018 (merging older duplicate entry with this one).

A165333 Numbers that eventually reach the fixed point 370 under "x -> sum of cubes of digits of x" (see A055012).

Original entry on oeis.org

7, 19, 34, 37, 43, 58, 67, 70, 73, 76, 85, 88, 91, 109, 118, 124, 139, 142, 145, 148, 154, 157, 166, 169, 175, 178, 181, 184, 187, 190, 193, 196, 214, 223, 226, 232, 241, 247, 259, 262, 268, 274, 277, 286, 295, 304, 307, 319, 322, 334, 340, 343, 346, 355, 358
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 17 2009

Keywords

Comments

A165330(a(n)) = 370;
Subsequence of A031179 and of A016777; a(n) mod 3 = 1.

Examples

			a(3)=34: 34 -> 3^3+4^3=91 -> 9^3+1=730 -> 7^3+3^3+0=370.

Crossrefs

Cf. A031179, A046197, A035504, A008585, A165334, A165335.

Programs

  • Mathematica
    f[n_] := Plus@@(IntegerDigits[n]^3); Trajectory[n_] := Most[NestWhileList[f, n, UnsameQ ,All]]; Select[Range[358], Last[Trajectory[#]] == 370&] (* Ant King, May 24 2013 *)

A165334 Numbers that eventually reach the fixed point 371 under "x -> sum of cubes of digits of x" (see A055012).

Original entry on oeis.org

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 50, 53, 56, 59, 62, 65, 68, 71, 80, 83, 86, 92, 95, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185, 188, 191
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 17 2009

Keywords

Comments

A165330(a(n)) = 371;
Subsequence of A031179;
complement of A165335 with respect to A016789; a(n) mod 3 = 2.

Examples

			a(10)=29: 29 -> 2^3+9^3=737 -> 2*7^3+3^3=713 -> 7^3+1+3^3=371.

Crossrefs

Cf. A031179, A046197, A035504, A008585, A165333.

Programs

  • Mathematica
    f[n_] := Plus@@(IntegerDigits[n]^3); Trajectory[n_] := Most[NestWhileList[f, n, UnsameQ ,All]]; Select[Range[191], Last[Trajectory[#]]==371 &] (* Ant King, May 24 2013 *)

A165335 Numbers that eventually reach the fixed point 407 under "x -> sum of cubes of digits of x" (see A055012).

Original entry on oeis.org

47, 74, 77, 89, 98, 407, 449, 470, 494, 578, 587, 668, 686, 704, 707, 740, 758, 770, 785, 788, 809, 857, 866, 875, 878, 887, 890, 908, 944, 980, 1124, 1139, 1142, 1148, 1157, 1175, 1178, 1184, 1187, 1193, 1214, 1241, 1319, 1367, 1376, 1391, 1412, 1418, 1421
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 17 2009

Keywords

Comments

A165330(a(n)) = 407.

Examples

			a(4)=89: 89 -> 8^3+9^3=1241 -> 1+2^3+4^3+1=74 -> 7^3+4^3=407.

Crossrefs

Subsequence of A031179.
Cf. A046197, A035504, A008585, A165333.

Programs

  • Mathematica
    f[n_] := Plus@@(IntegerDigits[n]^3); Trajectory[n_] := Most[NestWhileList[f,n,UnsameQ,All]]; Select[Range[1421], Last[Trajectory[#]]==407 &] (* Ant King, May 24 2013 *)
Select[Range[1500],FixedPoint[Total[IntegerDigits[#]^3]&,#,100]==407&] (* Harvey P. Dale, Apr 17 2020 *)

Formula

Complement of A165334 with respect to A016789; a(n) mod 3 = 2.

A165339 Numbers that eventually reach the cycle 919-1459 under "x -> sum of cubes of digits of x" (see A055012).

Original entry on oeis.org

49, 94, 199, 337, 373, 379, 397, 409, 478, 487, 490, 733, 739, 748, 784, 793, 847, 874, 904, 919, 937, 940, 973, 991, 1099, 1129, 1147, 1174, 1192, 1219, 1237, 1273, 1291, 1327, 1339, 1369, 1372, 1393, 1396, 1399, 1417, 1459, 1468, 1471, 1486, 1495, 1549
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 17 2009

Keywords

Comments

A165330(a(n)) = 919;
Subsequence of A165336.

Examples

			a(1)=49: 49 -> 4^3+9^3=793 -> 7^3+9^3+3^3=1099 -> 1+0+2*9^3=1459 -> 919 -> 1459 ... .

Crossrefs

Cf. A154820, A154877, A165330, A165336.

A165337 Numbers that eventually reach the cycle 136-244 under "x -> sum of cubes of digits of x" (see A055012).

Original entry on oeis.org

136, 163, 244, 316, 361, 424, 442, 613, 631, 1036, 1063, 1306, 1360, 1489, 1498, 1603, 1630, 1849, 1894, 1948, 1984, 2044, 2344, 2347, 2374, 2404, 2434, 2437, 2440, 2443, 2467, 2473, 2476, 2647, 2674, 2734, 2743, 2746, 2764, 3016, 3061, 3106, 3160, 3244
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 17 2009

Keywords

Comments

A165330(a(n)) = 136;
Subsequence of A165336.

Crossrefs

Cf. A154820, A154877, A165330, A165336, A165339.

A329386 Numbers k such that k + A055012(k) is a square.

Original entry on oeis.org

17, 104, 216, 260, 342, 392, 500, 518, 540, 590, 746, 830, 848, 1008, 1073, 1077, 1166, 1169, 1233, 1313, 1694, 1784, 1835, 1962, 1998, 2252, 2420, 2897, 3006, 3047, 3087, 3302, 3762, 4316, 4416, 4424, 4706, 4928, 5031, 5126, 5273, 5435, 6137, 6399, 6813, 7134, 7259, 7442, 7449, 7655, 7895, 7992
Offset: 1

Views

Author

Will Gosnell and Robert Israel, Nov 12 2019

Keywords

Examples

			a(3)=216 is a term because 216 + 2^3 + 1^3 + 6^3 = 441 = 21^2.

Links

Crossrefs

Cf. A055012, A329179.

Programs

  • Magma
    [k:k in [1..8000]|IsSquare(k+&+[c^3: c in Intseq(k)])]; // Marius A. Burtea, Nov 12 2019
  • Maple
    filter:= proc(n) local t;
  issqr( n + add(t^3,t=convert(n,base,10)));
end proc:
select(filter, [$1..10000]);
  • PARI
    A055012(n)=sum(i=1, #n=digits(n), n[i]^3)
is(n)=issquare(n + A055012(n)) \\ Charles R Greathouse IV, Jun 10 2020

A328293 Composite numbers k such that k+A055012(k) is the cube of a prime.

Original entry on oeis.org

34, 12025, 12130, 22789, 102952, 103039, 205222, 226019, 300176, 492203, 492221, 570760, 1030144, 1224376, 1224466, 2570470, 2684090, 3307264, 3868067, 3868157, 4329380, 4656049, 4656427, 5176537, 6966262, 6966403, 6966421, 7186697, 7186787, 7187318, 7187516, 7644406, 11694973, 12007691, 12008315
Offset: 1

Views

Author

Will Gosnell and Robert Israel, Oct 11 2019

Keywords

Comments

Computing the range of A055012(n) up to some upper limit using A179239 might help reduce the search space for finding terms. - David A. Corneth, Oct 11 2019

Examples

			a(3) = 12130 is included because 12130 is composite and 12130 + 1^3 + 2^3 + 1^3 + 3^3 + 0^3 = 12167 = 23^3 and 23 is prime.

Links

Crossrefs

Cf. A030078, A055012, A179239.

Programs

  • Maple
    filter:= proc(n) local x,t,F;
  if isprime(n) then return false fi;
  x:= n + add(t^3, t = convert(n,base,10));
  F:= ifactors(x)[2];
  nops(F)=1 and F[1][2]=3
end proc:
F:= proc(p,lastp) local n0;
  n0:= max(p^3 - 9^3*(1+ilog10(p^3)),lastp^3+1);
  select(filter, [$n0 .. p^3]);
end proc:
seq(op(F(ithprime(i),ithprime(i-1))),i=2..50);
  • PARI
    (scan(a,b)=forcomposite(n=max(a,b-9^3*(logint(b,10)+1))+1,b, n+A055012(n)==b && printf(n","))); forprime(p=1+o=2,234, scan(o^3,p^3)) \\ M. F. Hasler, Oct 11 2019

A082385 For each n append T(n), T(T(n)), T^3(n), ..., T^r(n), where T(n) = A055012(n) and r is the smallest integer such that T^r(n) is one of the following numbers: 1, 55, 136, 153, 160, 370, 371, 407, 919.

Original entry on oeis.org

1, 8, 512, 134, 92, 737, 713, 371, 27, 351, 153, 64, 280, 520, 133, 55, 125, 134, 92, 737, 713, 371, 216, 225, 141, 66, 432, 99, 1458, 702, 351, 153, 343, 118, 514, 190, 730, 370, 512, 134, 92, 737, 713, 371, 729, 1080, 513, 153, 1, 2, 8, 512, 134
Offset: 1

Views

Author

Cino Hilliard, Apr 13 2003

Keywords

Comments

Conjecture: The sequence always terminates with one of the following:(tested to n=1000000) 1,55,136,153,160,370,371,407,919 which eventually loop back to themselves. 1,153,370,371,407 loop back in 1 step and are the sum of the cubes of their digits. The others are 55,250,133,55. 136,244,136. 160,217,352,160. 919,1459,919. A046156, A046157 indicate this as a limit of possibilities of numbers that cubed digital roots roll back to the origional number. Proof? - Cino Hilliard, Apr 13 2003 Proof: In A055012 T. D. Noe notes that for n > 1999, A055012(n) < n. This means that by repeatedly applying A055012, we eventually reach a number smaller than 2000. As checked by Cino Hilliard, all numbers below 10^6 end in one of the listed cycles. - Stefan Steinerberger, Sep 05 2007

Crossrefs

Cf. A046156, A055012.

Programs

  • Mathematica
    a = {}; For[n = 1, n < 9, n++, j = Plus @@ IntegerDigits[n]^3; AppendTo[a, j]; While[ !MemberQ[{1, 55, 136, 153, 160, 370, 371, 407, 919}, j], j = Plus @@ (IntegerDigits[j]^3); AppendTo[a, j]]]; a
  • PARI
    digitcube2(m) = {y=0; for(x=1,m, digitcube(x) ) } digitcube(n) = { while(1, s=0; while(n > 0, d=n%10; s = s+d*d*d; n=floor(n/10); ); print1(s" "); if(s==1 || s==55 || s==153 || s==160 || s==370 || s==371 || s==407 || s==919 || s==136,break); n=s;) }

Extensions

Edited by Stefan Steinerberger, Sep 05 2007
Showing 1-10 of 65 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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