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A260191
Numbers m such that there exists no square whose base-m digit sum is binomial(m,2).
3
3, 5, 13, 17, 21, 29, 37, 45, 49, 53, 61, 65, 69, 77, 81, 85, 93, 101, 109, 113, 117, 125, 133, 141, 145, 149, 157, 165, 173, 177, 181, 189, 193, 197, 205, 209, 213, 221, 229, 237, 241, 245, 253, 257, 261, 269, 273, 277, 285, 293, 301, 305, 309, 317, 321, 325
OFFSET
1,1
COMMENTS
After the initial term a(1)=3 (see Example), this sequence consists of all numbers of the form (2j-1)*4^k+1 where j and k are positive integers.
For each term m > 3, no square has a base-m digit sum == binomial(m,2) (mod 4).
After the initial term a(1)=3, is this A249034?
EXAMPLE
No square has a base-3 digit sum of exactly binomial(3,2)=3, so 3 is in the sequence.
Binomial(5,2) = 10 == 2 (mod 4), but no square has a base-5 digit sum == 2 (mod 4), so there cannot be a square whose base-5 digit sum is 10; thus, 5 is in the sequence.
PROG
(Python)
from itertools import count, islice
def A260191_gen(startvalue=3): # generator of terms >= startvalue
c = max(startvalue, 3)
if c<=3: yield 3
for n in count(c+(c&1^1), 2):
if (~(m:=n-1>>1) & m-1).bit_length()&1:
yield n
A260191_list = list(islice(A260191_gen(), 20)) # Chai Wah Wu, Feb 26 2024
CROSSREFS
Sequence in context: A049282 A003625 A105900 * A094745 A072742 A076189
KEYWORD
nonn,base
AUTHOR
Jon E. Schoenfield, Jul 18 2015
STATUS
approved