An odd conjecture
What is the smallest odd number which can not be written as
Here, is integer and is prime.
Note : is to be excluded
The answer is 127.
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1 solution
Research:
A006285
Brute force:
Complement [ Table [ 2 n + 1 , { n , 2 0 0 } ] , Union [ Flatten [ Table [ 2 a + p , { a , 0 , 9 } , { p , Table [ p i , { i , 2 0 0 } ] } ] ] ] ] ⇒ { 1 2 7 , 1 4 9 , 2 5 1 , 3 3 1 , 3 3 7 , 3 7 3 }
Vallues below 10000 (above 10000 the values become frequent):
127,149,251,331,337,373,509,599,701,757,809,877,905,907,959,977,997,1019,1087,1199,1207,1211,1243,1259,1271,1477,1529,1541,1549,1589,1597,1619, 1649,1657,1719,1759,1777,1783,1807,1829,1859,1867,1927,1969,1973,1985,2171,2203,2213,2231,2263,2279,2293,2377,2429,2465,2503,2579,2669,2683, 2789,2843,2879,2909,2983,2993,2999,3029,3119,3149,3163,3181,3187,3215,3239,3299,3341,3343,3353,3431,3433,3505,3539,3637,3643,3665,3697,3739, 3779,3817,3845,3877,3967,3985,4001,4013,4063,4151,4153,4195,4229,4271,4311,4327,4503,4543,4567,4573,4589,4633,4649,4663,4691,4717,4781,4811, 4813,4841,4843,4855,4889,5077,5099,5125,5143,5303,5323,5405,5467,5557,5609,5617,5729,5731,5737,5755,5761,5771,5917,5923,5951,6001,6021,6065, 6073,6119,6161,6173,6193,6247,6269,6283,6403,6433,6449,6463,6509,6521,6535,6539,6547,6637,6659,6673,6731,6757,6791,6821,6853,6869,6883,6941, 7109,7151,7169,7177,7199,7267,7289,7297,7319,7331,7343,7379,7387,7389,7393,7405,7417,7431,7517,7535,7547,7583,7603,7747,7753,7783,7799,7807, 7811,7813,7841,7867,7901,7913,7961,8023,8031,8087,8107,8111,8141,8159,8257,8287,8363,8387,8399,8411,8429,8467,8527,8563,8587,8621,8669,8719, 8789,8831,8849,8861,8873,8887,8915,8921,8923,8929,8981,9101,9115,9239,9307,9371,9391,9431,9457,9473,9517,9521,9557,9569,9581,9613,9641,9787, 9809,9907,9929,9941 and 9959.