A038474 -id:A038474 - cp's OEIS frontend

A038475 Sums of 3 distinct powers of 5.

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

Olivier Gérard

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

Base 5 interpretation of A038445.

Cf. A000351, A038474, A038476, A038477.

Sort[Plus @@@ Subsets[5^Range[0, 7], {3}]] (* Amiram Eldar, Jul 13 2022 *)

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

Offset corrected by Amiram Eldar, Jul 13 2022

A038476 Sums of 4 distinct powers of 5.

Original entry on oeis.org

156, 656, 756, 776, 780, 3156, 3256, 3276, 3280, 3756, 3776, 3780, 3876, 3880, 3900, 15656, 15756, 15776, 15780, 16256, 16276, 16280, 16376, 16380, 16400, 18756, 18776, 18780, 18876, 18880, 18900, 19376, 19380, 19400, 19500, 78156, 78256, 78276, 78280, 78756, 78776, 78780

Offset: 1

Olivier Gérard

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

Base 5 interpretation of A038446.

Cf. A000351, A038474, A038475, A038477.

With[{upto=80000},Select[Total/@Subsets[5^Range[0,Floor[Surd[upto-31,5]]],{4}],#<=upto&]]//Union (* Harvey P. Dale, Mar 13 2019 *)

Offset corrected by Amiram Eldar, Jul 13 2022

A038477 Sums of 5 distinct powers of 5.

Original entry on oeis.org

781, 3281, 3781, 3881, 3901, 3905, 15781, 16281, 16381, 16401, 16405, 18781, 18881, 18901, 18905, 19381, 19401, 19405, 19501, 19505, 19525, 78281, 78781, 78881, 78901, 78905, 81281, 81381, 81401, 81405, 81881, 81901, 81905, 82001, 82005, 82025, 93781, 93881, 93901

Offset: 1

Olivier Gérard

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

Base 5 interpretation of A038447.

Cf. A000351, A038474, A038475, A038476.

Union[Total[5^#]&/@Subsets[Range[0,8],{5}]] (* Harvey P. Dale, Nov 15 2012 *)

from itertools import islice
def A038477_gen(): # generator of terms
    yield int(bin(n:=31)[2:],5)
    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:],5)
A038477_list = list(islice(A038477_gen(),30)) # Chai Wah Wu, Apr 05 2025

Offset corrected by Amiram Eldar, Jul 13 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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A038475 Sums of 3 distinct powers of 5.

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A038476 Sums of 4 distinct powers of 5.

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A038477 Sums of 5 distinct powers of 5.

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

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