A092739 Numbers n such that n*(n+1)/2 is the juxtaposition of two identical strings in binary representation.

2, 4, 5, 8, 9, 16, 17, 32, 33, 44, 64, 65, 90, 128, 129, 171, 256, 257, 512, 513, 702, 1024, 1025, 2048, 2049, 2732, 4096, 4097, 5542, 8192, 8193, 10923, 16384, 16385, 17515, 22939, 32768, 32769, 40050, 43361, 65536, 65537, 131072, 131073, 174764

Offset

1,1

Comments

2^n are terms for n>0 (A000079), 2^n + 1 are terms for n>1 (A000051).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..100

Example

17*(17+1)/2= 153 = 9*2^4 + 9 -> '10011001' -> '1001''1001', therefore 17 is a term.

Mathematica

tisbQ[n_]:=Module[{idn=IntegerDigits[(n(n+1))/2, 2], len}, len=Length[idn]; EvenQ[ len]&&Take[idn, len/2]==Take[idn, -len/2]]; Select[Range[ 180000], tisbQ] (* Harvey P. Dale, Aug 08 2016 *)

Prog

(PARI) is(n)=my(L=#binary(n*=(n+1)/2)\2); n>>L==bitand(n, 2^L-1) \\ Charles R Greathouse IV, Mar 29 2013

Crossrefs

Cf. A020330, A000217, A007088.

Sequence in context: A350356 A333256 A227369 * A277010 A101394 A095031

Adjacent sequences: A092736 A092737 A092738 * A092740 A092741 A092742

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 12 2004

Status

approved