Claims

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1993_01_01_freud: Freud's 1993 note builds, for N = 144y - 12, a set of 76y - 7 integers up to N with no member a sum of consecutive members, so the answer is no; accepted on the site's credit and the refereed paper that builds on it.

1996_05_01_coppersmith_phillips: Theorem 2.1 of Coppersmith and Phillips (SIAM J. Discrete Math. 1996) gives a set of 13N/24 - O(1) integers up to N with no consecutive-sum member, a second disproof, beside the upper bound of Theorem 3.7; accepted as refereed.

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