Search: id:A001032
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%I A001032 M1996 N0787
%S A001032 1,2,11,23,24,26,33,47,49,50,59,73,74,88,96,97,107,121,122,146,169,177,
%T A001032 184,191,193,194,218,239,241,242,249,289,297,299,311,312,313,337,338,
%U A001032 347,352,361,362,376,383,393,407,409,431,443,457,458,479,481,491,506
%N A001032 Numbers n such that sum of squares of n consecutive integers >= 1 is 
               a square.
%C A001032 It was shown by Watson (and again by Ljunggren) that if 0^2 + 1^2 + ... 
               + r^2 is a square then r = 0, 1 or 24.
%C A001032 The terms up to 1391 are == 0, 1, 2, 9, 11, 16, 23 mod 24. Start number 
               is in A007475(n). Square root of sum is in A076215(n). - Ralf Stephan 
               (ralf(AT)ark.in-berlin.de), Nov 04 2002
%C A001032 The solutions in the case n=2 are in A001652 or A082291.
%D A001032 U. Alfred, Consecutive integers whose sum of squares is a perfect square, 
               Math. Mag., 37 (1964), 19-32.
%D A001032 L. Beeckmans, Squares expressible as sum of consecutive squares, Amer. 
               Math. Monthly, 101 (1994), 437-442.
%D A001032 W. Ljunggren, New solution of a problem proposed by E. Lucas, Norsk Mat. 
               Tid. 34 (1952), 65-72.
%D A001032 S. Philipp, Note on consecutive integers whose sum of squares is a perfect 
               square, Math. Mag., 37 (1964), 218-220.
%D A001032 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001032 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001032 G. N. Watson, The problem of the square pyramid, Messenger Math. 48, 
               1-22, 1918.
%H A001032 T. D. Noe, <a href="b001032.txt">Table of n, a(n) for n=1..128</a>
%H A001032 K. S. Brown, <a href="http://www.mathpages.com/home/kmath147.htm">Sum 
               of Consecutive Nth Powers Equals an Nth Power</a>
%H A001032 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CannonballProblem.html">Cannonball Problem</a>
%H A001032 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%e A001032 3^2 + 4^2 = 5^2, with two consecutive terms, so 2 is in the sequence.
%Y A001032 Cf. A007475, A076215.
%Y A001032 Cf. A097812 (n^2 is the sum of two or more consecutive squares).
%Y A001032 Sequence in context: A118594 A018351 A004642 this_sequence A066079 A045386 
               A084354
%Y A001032 Adjacent sequences: A001029 A001030 A001031 this_sequence A001033 A001034 
               A001035
%K A001032 nonn,easy,nice
%O A001032 1,2
%A A001032 N. J. A. Sloane (njas(AT)research.att.com).
%E A001032 Corrected by T. D. Noe (noe(AT)sspectra.com), Aug 25 2004

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