A385486 -id:A385486 - cp's OEIS frontend

A385483 Where records occur in A385482.

1, 3, 7, 11, 13, 19, 103, 391, 1811, 3589, 5147, 6683, 21883, 46159, 64133, 149839, 151013, 318377, 650543, 1279211, 42559939, 43120271, 55201423, 198069181, 265237811, 929670011, 930260173, 1879562281, 3320654641, 5390681357, 52883996713, 78842843063, 250434427519

Offset: 1

Amiram Eldar, Jun 30 2025

Amiram Eldar, Table of n, a(n) for n = 1..40

Cf. A049445, A144364 (decimal analog), A385482, A385484 (record values), A385486.

f[n_] := Module[{m = n, k = 1}, While[!Divisible[m, DigitSum[m, 2]], m += n; k++]; k];
seq[lim_] := Module[{s = {}, fm = -1, fi}, Do[fi = f[i]; If[fi > fm, fm = fi; AppendTo[s, i]], {i, 1, lim}]; s]; seq[10^4]

f(n) = {my(m = n, k = 1); while(m % hammingweight(m), m += n; k++); k;}
list(lim) = my(fm = -1, fi); for(i = 1, lim, fi = f(i); if(fi > fm, fm = fi; print1(i, ", ")));

A385482(a(n)) = A385484(n).

A385485 a(n) is the least number k such that k*n is not a binary Niven number (A049445).

Original entry on oeis.org

3, 7, 1, 7, 1, 5, 1, 7, 1, 3, 1, 29, 1, 1, 1, 7, 1, 3, 1, 5, 3, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 7, 1, 3, 1, 13, 1, 1, 1, 5, 1, 5, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 17, 1, 1, 1, 7, 1, 3, 1, 7, 3, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 5, 3, 1, 1, 17, 1

Offset: 1

Amiram Eldar, Jun 30 2025

All the terms are odd numbers because if k is even and k*n is not a binary Niven number then so is k*n/2, since A000120(k*n) = A000120(k*n/2).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000120, A049445, A065878, A144262 (decimal analog), A385482, A385486 (indices of records), A385487 (record values).

a[n_] := Module[{m = n, k = 1}, While[Divisible[m, DigitSum[m, 2]], m += 2*n; k += 2]; k]; Array[a, 100]

a(n) = {my(m = n, k = 1); while(!(m % hammingweight(m)), m += 2*n; k += 2); k;}

from itertools import count
def a(n): return next(k for k in count(1) if (m:=k*n)%m.bit_count() != 0)
print([a(n) for n in range(1, 86)]) # Michael S. Branicky, Jun 30 2025

a(n) = 1 if and only if n is in A065878.

A385487 Records in A385485.

Original entry on oeis.org

3, 7, 29, 65, 69, 81, 257, 259, 4097, 4113, 4129, 262145, 262149, 1048577, 1048583, 16777217, 16777219, 38347927, 214748365, 214748369, 4294967297, 4294967299, 68719476737, 68719476769, 1099511627777, 4398046511105, 4398046511109

Offset: 1

Amiram Eldar, Jun 30 2025

Chai Wah Wu, Table of n, a(n) for n = 1..27

Cf. A049445, A144375 (decimal analog), A385484, A385485, A385486 (indices of records).

f[n_] := Module[{m = n, k = 1}, While[Divisible[m, DigitSum[m, 2]], m += 2*n; k += 2]; k];
seq[lim_] := Module[{s = {}, fm = -1, fi}, Do[fi = f[i]; If[fi > fm, fm = fi; AppendTo[s, fi]], {i, 1, lim}]; s]; seq[10^4]

f(n) = {my(m = n, k = 1); while(!(m % hammingweight(m)), m += 2*n; k += 2); k;}
list(lim) = my(fm = -1, fi); for(i = 1, lim, fi = f(i); if(fi > fm, fm = fi; print1(fi, ", ")));

a(n) = A385485(A385486(n)).

a(21)-a(27) from Chai Wah Wu, Jul 02 2025

cp's OEIS Frontend

A385483 Where records occur in A385482.

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A385485 a(n) is the least number k such that k*n is not a binary Niven number (A049445).

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A385487 Records in A385485.

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