A212222
Integers whose sum of digits in base b is the same for every prime b up to 11.
Original entry on oeis.org
0, 1, 1386, 1387, 485353, 981435, 4423035, 14187855, 19652536, 19652537, 19654636, 19654637, 23059876, 23059877, 23063359, 23837177, 25009516, 25009517, 41185278, 41185279, 41409018, 41409019, 49650315, 50262556, 50262557, 58622956, 58622957, 58623315
Offset: 1
1386 = 10101101010_2 = 1220100_3 = 21021_5 = 4020_7 = 1050_11. In each of these bases, the sum of the digits is 6.
A335839
Integers whose sum of digits in base b is the same for every prime b up to 13.
Original entry on oeis.org
0, 1, 2007986541, 2834822783, 31939595966, 33952616126, 42737313983, 44878987167, 309231463167, 318362221465, 415332522143, 881935644447, 1898245489647, 2077690289610, 2077690289611, 2153926044391, 3998461033469, 4285034622330, 4285034622331, 4294899857375
Offset: 1
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.
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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
A212223
a(n) is the least integer greater than 1 whose expansion in prime bases 2 to prime(n) have equal sum of digits.
Original entry on oeis.org
2, 6, 6, 882, 1386, 2007986541, 70911040973874056146188543
Offset: 1
a(5) = 1386 because that number has the same sum of digits in the first 5 prime bases 2, 3, 5, 7, 11 (see A212222 and A000040).
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f[n_] := Block[{p = Prime@ Range@ n, k = 2}, While[ Length[ Union[ Total@# & /@ IntegerDigits[k, p]]] != 1, k++]; k] (* Robert G. Wilson v, Oct 24 2014 *)
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isok(n, k) = my(s=hammingweight(k)); forprime (b=3, prime(n), if (sumdigits(k, b) != s, return (0))); return (1);
a(n) = my(k=2); while (!isok(n, k), k++); k; \\ Michel Marcus, Jun 08 2021
A345296
Integers whose sum of digits in base b is the same for every prime b up to 17.
Original entry on oeis.org
0, 1, 70911040973874056146188543, 77332999599545910254098143, 139857575920160383360253101
Offset: 1
77332999599545910254098143 = 11111111110111111001100100111011111011111110101111110010001010111101111101011011011111_2 =
1022220111022022121010102021222111100222120112011112120_3 = 10124120314223101043140143200022120033_5 = 3300561310042202241132326120022_7 = 7940063801000011830000282_11 = 1B101304100834600A304201_13 = 120802053643008116067_17. In these bases, the sum of digits is 63, so 77332999599545910254098143 is a term.
Showing 1-4 of 4 results.
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