A235490 Numbers such that none of their prime factors share common 1-bits in the same bit-position and when added (or "ored" or "xored") together, yield a term of A000225 (a binary "repunit").

1, 3, 7, 10, 26, 31, 58, 122, 127, 1018, 2042, 8186, 8191, 32762, 131071, 524287, 2097146, 8388602, 33554426, 1073741818, 2147483647, 2305843009213693951, 618970019642690137449562111, 39614081257132168796771975162, 162259276829213363391578010288127, 166153499473114484112975882535043066

Offset

1,2

Comments

a(1) = 1 is included on the grounds that it has no prime factors, thus A001414(1)=0, and 0 is one of the terms of A000225, marking the "repunit of length zero".

After 1, the sequence is a union of A000668 (Mersenne primes) and semiprimes of the form 2*A050415. The terms were constructed from the data given in those two entries.

Links

Table of n, a(n) for n=1..26.

Example

7 is included, because it is a prime, and repunit in base-2: '111'.
10 is included, as 10=2*5, and when we add 2 ('10' in binary) and 5 ('101' in binary), we also get 7 ('111' in binary), without producing any carries.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A235490 (MATCHING-POS 1 1 (lambda (n) (or (= 1 n) (and (= (A001414 n) (A072593 n)) (pow2? (1+ (A001414 n))))))))
(define (pow2? n) (let loop ((n n) (i 0)) (cond ((zero? n) #f) ((odd? n) (and (= 1 n) i)) (else (loop (/ n 2) (1+ i))))))

Crossrefs

Subsequence of A235050.

Cf. A000225, A000668, A050415, A001414, A072593, A178910, A227843.

Cf. also A235488, A230492, A235032, A050376.

Sequence in context: A024464 A127277 A302704 * A041437 A302279 A041525

Adjacent sequences: A235487 A235488 A235489 * A235491 A235492 A235493

Keyword

nonn,base

Author

Antti Karttunen, Jan 22 2014

Status

approved