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.

Previous Showing 11-17 of 17 results.

A038475 Sums of 3 distinct powers of 5.

Original entry on oeis.org

31, 131, 151, 155, 631, 651, 655, 751, 755, 775, 3131, 3151, 3155, 3251, 3255, 3275, 3751, 3755, 3775, 3875, 15631, 15651, 15655, 15751, 15755, 15775, 16251, 16255, 16275, 16375, 18751, 18755, 18775, 18875, 19375, 78131, 78151, 78155, 78251, 78255, 78275, 78751
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base 5 interpretation of A038445.
Cf. A000351, A038474, A038476, A038477.

Programs

  • Mathematica
    Sort[Plus @@@ Subsets[5^Range[0, 7], {3}]] (* Amiram Eldar, Jul 13 2022 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038475(n): return 5**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+5**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+5**(m+t+1) # Chai Wah Wu, Apr 04 2025

Extensions

Offset corrected by Amiram Eldar, Jul 13 2022

A038479 Sums of 3 distinct powers of 6.

Original entry on oeis.org

43, 223, 253, 258, 1303, 1333, 1338, 1513, 1518, 1548, 7783, 7813, 7818, 7993, 7998, 8028, 9073, 9078, 9108, 9288, 46663, 46693, 46698, 46873, 46878, 46908, 47953, 47958, 47988, 48168, 54433, 54438, 54468, 54648, 55728, 279943, 279973, 279978, 280153, 280158, 280188
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base-6 interpretation of A038445.
Cf. A000400, A038478, A038480.

Programs

  • Maple
    N:= 9: # to get all terms < 6^(N+1)
seq(seq(seq(6^i+6^j+6^k,k=0..j-1),j=1..i-1),i=2..N);
  • Mathematica
    Union[Total/@Subsets[6^Range[0,8],{3}]] (* Harvey P. Dale, May 17 2011 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038479(n): return 6**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+6**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+6**(m+t+1) # Chai Wah Wu, Apr 05 2025

Extensions

Offset changed by Robert Israel, May 08 2018

A038485 Sums of 3 distinct powers of 8.

Original entry on oeis.org

73, 521, 577, 584, 4105, 4161, 4168, 4609, 4616, 4672, 32777, 32833, 32840, 33281, 33288, 33344, 36865, 36872, 36928, 37376, 262153, 262209, 262216, 262657, 262664, 262720, 266241, 266248, 266304, 266752, 294913, 294920, 294976, 295424, 299008, 2097161, 2097217
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base-8 interpretation of A038445.
Cf. A001018, A038484, A038486.

Programs

  • Mathematica
    Take[Union[Total/@Subsets[8^Range[0,10],{3}]],40] (* Harvey P. Dale, Jan 31 2016 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038485(n): return (1<<3*((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2)))+(1<<3*((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1)))+(1<<3*(m+t+1)) # Chai Wah Wu, Apr 05 2025

Extensions

Offset corrected by Amiram Eldar, Jul 14 2022

A038482 Sums of 3 distinct powers of 7.

Original entry on oeis.org

57, 351, 393, 399, 2409, 2451, 2457, 2745, 2751, 2793, 16815, 16857, 16863, 17151, 17157, 17199, 19209, 19215, 19257, 19551, 117657, 117699, 117705, 117993, 117999, 118041, 120051, 120057, 120099, 120393, 134457, 134463, 134505, 134799, 136857, 823551, 823593
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base-7 interpretation of A038445.
Cf. A000420, A038481, A038483.

Programs

  • Mathematica
    Union[Total/@Subsets[7^Range[0,10],{3}]] (* Harvey P. Dale, May 06 2014 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038482(n): return 7**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+7**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+7**(m+t+1) # Chai Wah Wu, Apr 05 2025

Extensions

Offset corrected by Amiram Eldar, Jul 14 2022

A038488 Sums of 3 distinct powers of 9.

Original entry on oeis.org

91, 739, 811, 819, 6571, 6643, 6651, 7291, 7299, 7371, 59059, 59131, 59139, 59779, 59787, 59859, 65611, 65619, 65691, 66339, 531451, 531523, 531531, 532171, 532179, 532251, 538003, 538011, 538083, 538731, 590491, 590499, 590571, 591219, 597051, 4782979, 4783051
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base-9 interpretation of A038445.
Cf. A001019, A038487, A038489.

Programs

  • Mathematica
    Sort[Plus @@@ Subsets[9^Range[0, 6], {3}]] (* Amiram Eldar, Jul 14 2022 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038488(n): return 9**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+9**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+9**(m+t+1) # Chai Wah Wu, Apr 05 2025

Extensions

Offset corrected by Amiram Eldar, Jul 14 2022

A038493 Sums of 3 distinct powers of 12.

Original entry on oeis.org

157, 1741, 1873, 1884, 20749, 20881, 20892, 22465, 22476, 22608, 248845, 248977, 248988, 250561, 250572, 250704, 269569, 269580, 269712, 271296, 2985997, 2986129, 2986140, 2987713, 2987724, 2987856, 3006721, 3006732, 3006864, 3008448, 3234817, 3234828, 3234960
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base-12 interpretation of A038445.
Cf. A001021, A038492.

Programs

  • Mathematica
    Union[Total/@Subsets[12^Range[0,6],{3}]] (* Harvey P. Dale, Sep 06 2012 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038493(n): return 12**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+12**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+12**(m+t+1) # Chai Wah Wu, Apr 04 2025

Extensions

Offset corrected by Amiram Eldar, Jul 14 2022

A038491 Sums of 3 distinct powers of 11.

Original entry on oeis.org

133, 1343, 1453, 1463, 14653, 14763, 14773, 15973, 15983, 16093, 161063, 161173, 161183, 162383, 162393, 162503, 175693, 175703, 175813, 177023, 1771573, 1771683, 1771693, 1772893, 1772903, 1773013, 1786203, 1786213, 1786323
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base-11 interpretation of A038445.
Cf. A000217, A000292.

Programs

  • Maple
    seq(seq(seq(11^a+11^b+11^c,c=0..b-1),b=1..a-1),a=2..10); # Robert Israel, Dec 23 2016
  • Mathematica
    TakeWhile[#, # <= 1800000 &] &@ Sort@ Map[Total, 11^Subsets[Range[0, 8], {3}]] (* Michael De Vlieger, Dec 23 2016 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038491(n): return 11**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+11**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+11**(m+t+1) # Chai Wah Wu, Apr 05 2025

Formula

a(A000292(m+1)+k) = a(A000292(m)+k) + 10*11^(m+2) for 0<=k<=A000217(m). - Robert Israel, Dec 23 2016
Previous Showing 11-17 of 17 results.

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