A335839 Integers whose sum of digits in base b is the same for every prime b up to 13.

0, 1, 2007986541, 2834822783, 31939595966, 33952616126, 42737313983, 44878987167, 309231463167, 318362221465, 415332522143, 881935644447, 1898245489647, 2077690289610, 2077690289611, 2153926044391, 3998461033469, 4285034622330, 4285034622331, 4294899857375

Offset: 1

Author

Thomas König, Sep 13 2020

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Thomas König, Table of n, a(n) for n = 1..19840

Crossrefs

Cf. A212223, A212222, A135127, A135121, A037301.

Programs

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