This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A235490 #12 Feb 01 2014 14:52:13
%S A235490 1,3,7,10,26,31,58,122,127,1018,2042,8186,8191,32762,131071,524287,
%T A235490 2097146,8388602,33554426,1073741818,2147483647,2305843009213693951,
%U A235490 618970019642690137449562111,39614081257132168796771975162,162259276829213363391578010288127,166153499473114484112975882535043066
%N 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").
%C A235490 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".
%C A235490 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.
%e A235490 7 is included, because it is a prime, and repunit in base-2: '111'.
%e A235490 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.
%o A235490 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A235490 (define A235490 (MATCHING-POS 1 1 (lambda (n) (or (= 1 n) (and (= (A001414 n) (A072593 n)) (pow2? (1+ (A001414 n))))))))
%o A235490 (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))))))
%Y A235490 Subsequence of A235050.
%Y A235490 Cf. A000225, A000668, A050415, A001414, A072593, A178910, A227843.
%Y A235490 Cf. also A235488, A230492, A235032, A050376.
%K A235490 nonn,base
%O A235490 1,2
%A A235490 _Antti Karttunen_, Jan 22 2014