A158789 a(n) is the smallest positive multiple of 2n-1 that contains the binary representation of n in its binary representation and that is a palindrome when written in binary.

1, 9, 15, 231, 27, 99, 455, 195, 51, 2565, 189, 2553, 1675, 189, 7163, 15903, 99, 5285, 2553, 10725, 21525, 3483, 495, 17249, 6419, 2805, 30263, 10725, 30039, 6077, 31903, 3591, 195, 1675, 116679, 108843, 2409, 52275, 231, 361741, 38313, 27307, 2805

Offset

1,2

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

3 = 11_2. Checking the multiples of 5 (which is 3*2-1) to determine the 3rd term of the sequence, we have: 1*5 = 5 = 101_2, which is a palindrome, but does not contain the substring '11'. 2*5 = 10 = 1010_2, which neither contains '11' nor is a palindrome. 3*5 = 15 = 1111_2, which is a palindrome and does contain the substring '11'. So a(3) = 15.

Maple

ispal := proc(L) local i; for i from 1 to nops(L)/2 do if op(i, L) <> op(-i, L) then RETURN(false) ; fi; od: RETURN(true) ; end: A158789 := proc(n) local k, adgs, a, ndgs; ndgs := convert(n, base, 2) ; for k from 1 do a := k*(2*n-1) ; adgs := convert(a, base, 2) ; if verify(ndgs, adgs, 'sublist') then if ispal(adgs) then RETURN(a) ; fi; fi; od: end: seq(A158789(n), n=1..55) ; # R. J. Mathar, Apr 16 2009

Crossrefs

Sequence in context: A124274 A075134 A316744 * A355654 A100241 A078794

Adjacent sequences: A158786 A158787 A158788 * A158790 A158791 A158792

Keyword

nonn,base

Author

Leroy Quet, Mar 26 2009

Extensions

More terms from R. J. Mathar, Apr 16 2009

Status

approved