A038487 -id:A038487 - cp's OEIS frontend

A038488 Sums of 3 distinct powers of 9.

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

Olivier Gérard

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

Base-9 interpretation of A038445.

Cf. A001019, A038487, A038489.

Sort[Plus @@@ Subsets[9^Range[0, 6], {3}]] (* Amiram Eldar, Jul 14 2022 *)

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

Offset corrected by Amiram Eldar, Jul 14 2022

A038489 Sums of 4 distinct powers of 9.

Original entry on oeis.org

820, 6652, 7300, 7372, 7380, 59140, 59788, 59860, 59868, 65620, 65692, 65700, 66340, 66348, 66420, 531532, 532180, 532252, 532260, 538012, 538084, 538092, 538732, 538740, 538812, 590500, 590572, 590580, 591220, 591228, 591300, 597052, 597060, 597132, 597780, 4783060

Offset: 1

Olivier Gérard

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

Base-9 interpretation of A038446.

Cf. A001019, A038487, A038488.

Sort[Plus @@@ Subsets[9^Range[0, 6], {4}]] (* Amiram Eldar, Jul 14 2022 *)

from itertools import islice
def A038489_gen(): # generator of terms
    yield int(bin(n:=15)[2:],9)
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:],9)
A038489_list = list(islice(A038489_gen(),30)) # Chai Wah Wu, Apr 05 2025

Offset corrected by Amiram Eldar, Jul 14 2022

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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A038488 Sums of 3 distinct powers of 9.

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A038489 Sums of 4 distinct powers of 9.

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

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