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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
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
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 12 2004
STATUS
approved