A038444 -id:A038444 - cp's OEIS frontend

A038487 Sums of two distinct powers of 9.

10, 82, 90, 730, 738, 810, 6562, 6570, 6642, 7290, 59050, 59058, 59130, 59778, 65610, 531442, 531450, 531522, 532170, 538002, 590490, 4782970, 4782978, 4783050, 4783698, 4789530, 4842018, 5314410, 43046722, 43046730, 43046802, 43047450, 43053282

Offset: 1

Olivier Gérard

Robert Israel, Table of n, a(n) for n = 1..10001

Base 9 interpretation of A038444.

N:= 10^10: # to get all terms <= N
{seq(seq(9^a+9^b,b=0..a-1),a=1..floor(log[9](N)))}; # Robert Israel, Aug 31 2014

Total/@Subsets[9^Range[0,10],{2}]//Union (* Harvey P. Dale, Aug 25 2023 *)

for(a=0,19,for(b=0,a-1,print1(9^a+9^b,","))) \\ M. F. Hasler, Aug 31 2014

from math import isqrt
def A038487(n): return 9**(m:=isqrt(n<<3)+1>>1)+9**(n-1-(m*(m-1)>>1)) # Chai Wah Wu, Apr 05 2025

a(n)=9^A002024(n)+9^A002262(n). - M. F. Hasler, Aug 31 2014

More terms from Vincenzo Librandi, Aug 06 2009
Corrected by Harvey P. Dale, Aug 31 2014
Offset changed from 0 to 1 by M. F. Hasler, Aug 31 2014

A038492 Sums of 2 distinct powers of 12.

Original entry on oeis.org

13, 145, 156, 1729, 1740, 1872, 20737, 20748, 20880, 22464, 248833, 248844, 248976, 250560, 269568, 2985985, 2985996, 2986128, 2987712, 3006720, 3234816, 35831809, 35831820, 35831952, 35833536, 35852544, 36080640, 38817792, 429981697, 429981708, 429981840, 429983424, 430002432, 430230528

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Base-12 interpretation of A038444.

Cf. A001021, A038493.

Take[Union[Plus@@@Subsets[12^Range[0,20],{2}]],50] (* Harvey P. Dale, Dec 16 2010 *)

from math import isqrt
def A038492(n): return 12**(m:=isqrt(n<<3)+1>>1)+12**(n-1-(m*(m-1)>>1)) # Chai Wah Wu, Apr 04 2025

More terms from Vincenzo Librandi, Aug 06 2009

Offset corrected by Amiram Eldar, Jul 14 2022

A038490 Sums of 2 distinct powers of 11.

Original entry on oeis.org

12, 122, 132, 1332, 1342, 1452, 14642, 14652, 14762, 15972, 161052, 161062, 161172, 162382, 175692, 1771562, 1771572, 1771682, 1772892, 1786202, 1932612, 19487172, 19487182, 19487292, 19488502, 19501812, 19648222, 21258732, 214358882, 214358892, 214359002, 214360212, 214373522, 214519932, 216130442

Offset: 1

Olivier Gérard

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

Base 11 interpretation of A038444.

seq(seq(11^i+11^j,i=0..j-1),j=1..10); # Robert Israel, Jun 21 2018

Take[Union[Plus@@@Subsets[11^Range[0,20],{2}]],50] (* Harvey P. Dale, Dec 16 2010 *)

from math import isqrt
def A038490(n): return 11**(m:=isqrt(n<<3)+1>>1)+11**(n-1-(m*(m-1)>>1)) # Chai Wah Wu, Apr 04 2025

More terms from Vincenzo Librandi, Aug 06 2009

a(33)=214373522 inserted by Robert Israel, Jun 21 2018

A371004 Fourth powers whose digital sum is also a fourth power.

Original entry on oeis.org

0, 1, 10000, 14641, 100000000, 104060401, 146410000, 1000000000000, 1004006004001, 1040604010000, 1464100000000, 4228599998736, 8670998958336, 9748688599521, 9948826238976, 12598637895936, 19226786746896, 19896452775936, 20699669996721, 23768199069696, 26599197668481

Offset: 1

Stefano Spezia, Mar 08 2024

Among the terms of this sequence, there are:
  the numbers of the form 10^(4*k) with k >= 0;
  the numbers of the form (10^i + 10^j)^4 with i > j >= 0.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Cf. A000583, A007953, A038444, A053057, A053058, A371047.

Select[Range[0,2500]^4, IntegerQ[DigitSum[#]^(1/4)]&]

a(n) = A371047(n)^4.

A371047 Numbers k such that the digital sum of k^4 is a fourth power.

Original entry on oeis.org

0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1100, 1434, 1716, 1767, 1776, 1884, 2094, 2112, 2133, 2208, 2271, 2292, 2298, 2514, 2544, 2556, 2604, 2628, 2892, 2919, 2922, 2976, 3006, 3018, 3066, 3078, 3096, 3111, 3126, 3138, 3144, 3159, 3162, 3492, 3498, 3504

Offset: 1

Stefano Spezia, Mar 09 2024

Stefano Spezia, Table of n, a(n) for n = 1..10000

Cf. A000583, A007953, A011557 (subsequence), A038444 (subsequence), A061910, A237525, A371004.

Select[Range[0,4000]^4,IntegerQ[DigitSum[#]^(1/4)]&]^(1/4)

a(n) = A371004(n)^(1/4).

A139369 Array read by antidiagonals, n-th sum of 2 distinct powers of k.

Original entry on oeis.org

3, 4, 5, 5, 10, 6, 6, 17, 12, 9, 7, 26, 20, 28, 10, 8, 37, 30, 65, 30, 12, 9, 50, 42, 126, 68, 36, 17, 10, 65, 56, 217, 130, 80, 82, 18, 11, 82, 72, 344, 222, 150, 257, 84, 20, 12, 101, 90, 513, 350, 252, 626, 260, 90, 24, 13, 122, 110, 730, 520, 392, 1297, 630, 272, 108

Offset: 1

Jonathan Vos Post, Jun 07 2008

n=2 column is A002522 n^2 + 1.

n=3 column is A002378 n*(n+1) Oblong (or pronic, promic, or heteromecic numbers).

			Array begins:
================================================================================
k....|.n=1.|.n=2.|.n=3.|..n=4.|..n=5.|..n=6.|...n=7.|...n=8.|..n=9.|.n=10|.OEIS.
================================================================================
k=2..|..3..|...5.|..6..|....9.|...10.|...12.|....17.|...18..|...20.|..24.|A018900
k=3..|..4..|..10.|.12..|...28.|...30.|...36.|....82.|...84..|...90.|..108|A038464
k=4..|..5..|..17.|.20..|...65.|...68.|...80.|...257.|..260..|..272.|..320|A038470
k=5..|..6..|..26.|.30..|..126.|..130.|..150.|...626.|..630..|..650.|..750|A038474
k=6..|..7..|..37.|.42..|..217.|..222.|..252.|..1297.|..1302.|.1332.|.1512|A038478
k=7..|..8..|..50.|.56..|..344.|..350.|..392.|..2402.|..2408.|.2450.|.2744|A038481
k=8..|..9..|..65.|.72..|..513.|..520.|..576.|..4097.|..4104.|.4160.|.4608|A038484
k=9..|.10..|..82.|.90..|..730.|..738.|..810.|..6562.|..6570.|.6642.|.7290|A038487
k=10.|.11..|.101.|.110.|.1001.|.1010.|.1100.|.10001.|.10010.|10100.|11000|A038444
k=11.|.12..|.122.|.132.|.1332.|.1342.|.1452.|.14642.|.14652.|14762.|15972|A038490
k=12.|.13..|.145.|.156.|.1729.|.1740.|.1872.|.20737.|.20748.|20880.|22464|A038492
================================================================================

Cf. A002378, A002522, A018900, A038464, A038470, A038474, A038478, A038481, A038484, A038487, A038444, A038490, A038492.

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A038487 Sums of two distinct powers of 9.

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A038492 Sums of 2 distinct powers of 12.

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A038490 Sums of 2 distinct powers of 11.

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A371004 Fourth powers whose digital sum is also a fourth power.

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A371047 Numbers k such that the digital sum of k^4 is a fourth power.

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A139369 Array read by antidiagonals, n-th sum of 2 distinct powers of k.

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