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A335839
Integers whose sum of digits in base b is the same for every prime b up to 13.
3
0, 1, 2007986541, 2834822783, 31939595966, 33952616126, 42737313983, 44878987167, 309231463167, 318362221465, 415332522143, 881935644447, 1898245489647, 2077690289610, 2077690289611, 2153926044391, 3998461033469, 4285034622330, 4285034622331, 4294899857375
OFFSET
1,3
COMMENTS
This is a subset of A212222 for bases 2, 3, 5, 7, 11, which is a subset of A135127 for bases 2, 3, 5, 7, which is a subset of A135121 for bases 2 ,3, 5, which is a subset of A037301 for bases 2, 3. The third term also occurs in A212223.
LINKS
EXAMPLE
31939595966 is 11101101111101111111000111010111110_2, 10001102220222120211202_3, 1010403014032331_5, 2210331041405_7, 12600084203_11 and 3020180615_13. In these bases, the sum of digits is 26, so 31939595966 is a term.
PROG
(Python)
def digsum(n, b):
s = 0
while n > 0:
n, d = n//b, n%b
s = s+d
return s
p = [2, 3, 5, 7, 11, 13]
n, a = 0, 0
while n <= 20:
s2, i = digsum(a, 2), 1
while i < len(p) and digsum(a, p[i]) == s2:
i = i+1
if i == len(p):
print(a, end = ", ")
n = n+1
a = a+1 # A.H.M. Smeets, May 16 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Thomas König, Sep 13 2020
STATUS
approved