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A391733
Numbers in whose binary expansion there is exactly one run of 1-bits with an odd length, while all other run of 1-bits are of an even length (or absent).
2
1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 22, 25, 26, 28, 31, 32, 35, 38, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 64, 67, 70, 76, 79, 88, 91, 94, 97, 98, 100, 103, 104, 107, 109, 110, 112, 115, 118, 121, 122, 124, 127, 128, 131, 134, 140, 143, 152, 155, 158, 176, 179, 182, 188, 191, 193, 194, 196, 199, 200, 203, 205, 206
OFFSET
1,2
COMMENTS
Numbers k such that A005940(1+k) is in A229125.
If n is a term, then 2*n is also a term, and vice versa.
FORMULA
{k such that A358769(A005940(1+k)) = 1}.
EXAMPLE
4, in binary A007088(4) = 100, has one run of 1-bits, with length 1 (which is an odd number), therefore 4 is included in this sequence.
103, in binary 1100111, has one run of two 1-bits and one run of three 1-bits, therefore 103 is included as a term, as there is only one run with an odd length.
107, in binary 1101011, has two runs of two 1-bits and only one run of single 1-bit, thus only one run of 1's with an odd length, therefore 107 is included as a term.
PROG
(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A358769(n) = isprime(core(n));
is_A391733(k) = A358769(A005940(1+k));
CROSSREFS
Subsequences: A000079, (at least) the even terms of A000396\{6}, A000668, A233868.
Sequence in context: A080308 A089559 A165741 * A238989 A093696 A190851
KEYWORD
nonn,base,easy
AUTHOR
Antti Karttunen, Dec 29 2025
STATUS
approved