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A092739 Numbers n such that n*(n+1)/2 is the juxtaposition of two identical strings in binary representation. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A200947 A333256 A227369 * A277010 A101394 A095031

Adjacent sequences:  A092736 A092737 A092738 * A092740 A092741 A092742

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Apr 12 2004

STATUS

approved

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Last modified October 23 00:11 EDT 2021. Contains 348204 sequences. (Running on oeis4.)