This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A171886 #12 Apr 30 2014 21:08:07 %S A171886 0,1,2,3,5,6,7,9,10,14,15,17,20,21,27,28,29,31,35,36,44,45,49,54,55, %T A171886 65,66,71,77,78,90,91,97,104,105,119,120,121,127,135,136,152,153,161, %U A171886 170,171,189,190,199,209,210,230,231,241,252,253,275,276,279,287,299 %N A171886 Numbers n such that A008949(n) is a power of 2. %C A171886 Partial sums of binomial coefficients were considered in section 2.2 of the 1964 paper by Leech. The presence of the number 279 corresponds to the existence of the Golay perfect code of length 23. %C A171886 In general, A000217(n+1)+i-1 is in this sequence IFF the first i items in row n of Pascal's triangle add up to a power of 2. %C A171886 Almost all members of this sequence are "trivial" terms of four types: A000217(i); A000217(i)+1, A000217(i)+i, and A000217(2i+1)+i for all integers i. 279 is the sole nontrivial term. %C A171886 The existence of members of this sequence is of course crucial in the study of the existence of perfect binary codes - see the references. - _N. J. A. Sloane_, Nov 24 2010 %C A171886 a(230) = 4097 is another nontrivial term, see example. - _Reinhard Zumkeller_, Aug 08 2013 %D A171886 M. R. Best, Perfect codes hardly exist. IEEE Trans. Inform. Theory 29 (1983), no. 3, 349-351. %D A171886 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag. %D A171886 John Leech, ``Some Sphere Packings in Higher Space'', Can. J. Math., 16 (1964), page 669. %D A171886 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977. %D A171886 A. Tietavainen, On the nonexistence of perfect codes over finite fields. SIAM J. Appl. Math. 24 (1973), 88-96. %D A171886 J. H. van Lint, A survey of perfect codes. Rocky Mountain J. Math. 5 (1975), 199-224. %D A171886 J. H. van Lint, Recent results on perfect codes and related topics, in Combinatorics (Proc. NATO Advanced Study Inst., Breukelen, 1974), pp. 158-178. Math. Centre Tracts, No. 55, Math. Centrum, Amsterdam, 1974. %H A171886 Reinhard Zumkeller, <a href="/A171886/b171886.txt">Table of n, a(n) for n = 1..10000</a> %H A171886 John Leech, <a href="http://www.cms.math.ca/cjm/v16/cjm1964v16.0657-0682.pdf">Some Sphere Packings in Higher Space</a> (PDF available from the publisher). %e A171886 17 is in the sequence because A008949(17)=16, which in turn is because the first 3 elements of row 5 of Pascal's triangle, 1+5+10, add up to 16. %e A171886 279 is in the sequence because the first 4 elements of row 24 of Pascal's triangle add up to 2^11: 1+23+253+1771=2048. %e A171886 4097 is in the sequence because the first 3 elements of row 91 of Pascal's triangle add up to 2^12: 1 + 90 + 4005 = 4096. - _Reinhard Zumkeller_, Aug 08 2013 %o A171886 (Haskell) %o A171886 import Data.List (elemIndices) %o A171886 a171886 n = a171886_list !! (n-1) %o A171886 a171886_list = elemIndices 1 $ map a209229 $ concat a008949_tabl %o A171886 -- _Reinhard Zumkeller_, Aug 08 2013 %Y A171886 Cf. A008949. %Y A171886 Cf. A209229. %K A171886 nonn %O A171886 1,3 %A A171886 _Robert Munafo_, Oct 16 2010 %E A171886 Edited by _N. J. A. Sloane_, Oct 18 2010 %E A171886 Offset changed by _Reinhard Zumkeller_, Aug 08 2013