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

Author

Reinhard Zumkeller, Apr 12 2004

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A020330, A000217, A007088.

Programs

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 *)

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