[go: up one dir, main page]

login
A227062
Numbers whose base-5 sum of digits is 5.
10
9, 13, 17, 21, 29, 33, 37, 41, 45, 53, 57, 61, 65, 77, 81, 85, 101, 105, 129, 133, 137, 141, 145, 153, 157, 161, 165, 177, 181, 185, 201, 205, 225, 253, 257, 261, 265, 277, 281, 285, 301, 305, 325, 377, 381, 385, 401, 405, 425, 501, 505, 525, 629, 633, 637
OFFSET
1,1
COMMENTS
All of the entries are odd.
Subsequence of A016813. - Michel Marcus, Sep 03 2013
In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..11613 (all terms with <= 15 base-5 digits)
EXAMPLE
The 5-ary expansion of 9 is (1,4), which has sum of digits 5.
The 5-ary expansion of 53 is (2,0,3), which has sum of digits 5.
10 is not on the list since the 5-ary expansion of 10 is (2,0), which has sum of digits 2 not 5.
MATHEMATICA
Select[Range@ 640, Total@ IntegerDigits[#, 5] == 5 &] (* Michael De Vlieger, Dec 23 2016 *)
PROG
(Sage) [i for i in [0..1000] if sum(Integer(i).digits(base=5))==5]
(PARI) select( is(n)=sumdigits(n, 5)==5, [1..999]) \\ M. F. Hasler, Dec 23 2016
(Python)
from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits_base5):
alst = []
for d in range(2, maxdigits_base5 + 1):
fulldigset = list("0"*(d-2) + "111112234")
for firstdig in "1234":
target_sum, restdigset = 5 - int(firstdig), fulldigset[:]
restdigset.remove(firstdig)
for p in multiset_permutations(restdigset, d-1):
if sum(map(int, p)) == target_sum:
alst.append(int(firstdig+"".join(p), 5))
if int(p[0]) == target_sum:
break
return alst
print(auptodigs(5)) # Michael S. Branicky, Sep 13 2021
(Python)
agen = A226636gen(sod=5, base=5) # generator of terms using code in A226636
print([next(agen) for n in range(1, 56)]) # Michael S. Branicky, Jul 10 2022
CROSSREFS
Cf. A226636 (b = 3), A226969 (b = 4), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10).
Sequence in context: A050109 A294357 A329388 * A134441 A174055 A273059
KEYWORD
nonn,base,easy
AUTHOR
Tom Edgar, Sep 01 2013
STATUS
approved