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 A108269 Numbers of the form (2*m - 1)*4^k where m >= 1, k >= 1. 6
 4, 12, 16, 20, 28, 36, 44, 48, 52, 60, 64, 68, 76, 80, 84, 92, 100, 108, 112, 116, 124, 132, 140, 144, 148, 156, 164, 172, 176, 180, 188, 192, 196, 204, 208, 212, 220, 228, 236, 240, 244, 252, 256, 260, 268, 272, 276, 284, 292, 300, 304, 308, 316, 320, 324, 332 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers of terms in nonnegative integer sequences the sum of which is never a square. The sum of a sequence of consecutive nonnegative integers starting with k is never a square for any k, if and only if the number of the terms in the sequence can be expressed as (2*m - 1) * 2^(2*n), m and n being any positive integers. (Proved by Alfred Vella, Jun 14 2005.) Odious and evil terms alternate. - Vladimir Shevelev, Jun 22 2009 Even numbers whose binary representation ends in an even number of zeros. - Amiram Eldar, Jan 12 2021 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = 6*n + O(log n). - Charles R Greathouse IV, Nov 03 2016 [Corrected by Amiram Eldar, Jan 12 2021] a(n) = 2 * A036554(n) = 4 * A003159(n). - Amiram Eldar, Jan 12 2021 EXAMPLE a( 1, 1 ) = 4, a( 2, 1) = 12, etc. For a( 1, 1 ): the sum of 4 consecutive nonnegative integers (4k+6, if the first term is k) is never a square. MATHEMATICA Select[2 * Range[200], EvenQ @ IntegerExponent[#, 2] &] (* Amiram Eldar, Jan 12 2021 *) PROG (PARI) is(n)=my(e=valuation(n, 2)); e>1 && e%2==0 \\ Charles R Greathouse IV, Nov 03 2016 CROSSREFS Intersection of A005843 and A003159. Cf. A000069, A001969, A036554. Sequence in context: A267958 A077770 A310566 * A081523 A310567 A310568 Adjacent sequences:  A108266 A108267 A108268 * A108270 A108271 A108272 KEYWORD nonn,easy AUTHOR Andras Erszegi (erszegi.andras(AT)chello.hu), May 30 2005 EXTENSIONS Entry revised by N. J. A. Sloane, Jun 26 2005 More terms from Amiram Eldar, Jan 12 2021 STATUS approved

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Last modified June 16 19:05 EDT 2021. Contains 345068 sequences. (Running on oeis4.)