$a_{10}=79$, 此时 $m∈{5, 6, 8, 9, 15, 21, 30, 38, 42, 4}$
$a_{20}=617$, 此时 $m∈{6,7,8,12,18,22,23,25,31,34,38,47,144,203,317,359,373,420,476,551}$
前20项：$ {3, 7, 23, 11, 13, 31, 43, 17, 61, 79, 103, 113, 89, 197, 163, 509, 571, 409, 929, 617}$ 这使我想起很久以前的一个类哥猜：奇数都可表为2的幂与一个素数之和。
忘了哪个数学家说的，这样的猜想随便可以提出无数多个。:L
5=4+1=2+3
7=4+3=2+5
9=8+1=4+5=2+7
11=8+3=4+7
13=8+5=2+11
15=8+7=4+11=2+13
17=16+1=4+13
19=16+3=8+11=2+17
21=16+5=8+13=4+17=2+19
23=16+7=4+19
25=8+17=2+23
27=16+11=8+19=4+23
29=16+13
31=8+23=2+29
33=32+1=16+17=4+29=2+31
35=32+3=16+19=4+31
37=32+5=8+29
39=32+7=16+23=8+31=2+37
41=4+37
43=32+11=2+41
45=32+13=16+29=8+37=4+41=2+43
47=16+31=4+43
49=32+17=8+41=2+47
51=32+19=8+43=4+47
53=16+37
55=32+23=8+47
57=16+41=4+53
59=16+43
61=32+29=8+53=2+59
63=32+31=16+47=4+59=2+61
65=64+1=4+61
67=64+3=8+59
69=32+37=16+53=8+61=2+67
71=64+7=4+67
73=32+41=2+71
75=64+11=32+43=16+59=8+67=4+71=2+73
77=64+13=16+61=4+73
79=32+47=8+71
81=64+17=8+73=2+79
83=64+19=16+67=4+79
85=32+53=2+83
87=64+23=16+71=8+79=4+83
89=16+73
91=32+59=8+83=2+89
93=64+29=32+61=4+89
95=64+31=16+79
97=8+89
99=32+67=16+83=2+97
101=4+97
103=32+71=2+101
105=64+41=32+73=16+89=8+97=4+101=2+103
107=64+43=4+103
109=8+101=2+107
111=64+47=32+79=8+103=4+107=2+109
hujunhua 发表于 2024-4-21 14:30
这使我想起很久以前的一个类哥猜：奇数都可表为2的幂与一个素数之和。
忘了哪个数学家说的，这样的猜想随便 ...
这是个假命题
A006285 Odd numbers not of form p + 2^k (de Polignac numbers).
f :=
Table[{2^x, n - 2^x}, {x,
Select]], PrimeQ &]}]; Select[
2Range@2500 - 1, Length@f[#] == 0 &]
{1,127,149,251,331,337,373,509,599,701,757,809,877,905,907,959,977,997,1019,1087,1199,1207,1211,1243,1259,1271,1477,1529,1541,1549,1589,1597,1619,1649,1657,1719,1759,1777,1783,1807,1829,1859,1867,1927,1969,1973,1985,2171,2203,2213,2231,2263,2279,2293,2377,2429,2465,2503,2579,2669,2683,2789,2843,2879,2909,2983,2993,2999,3029,3119,3149,3163,3181,3187,3215,3239,3299,3341,3343,3353,3431,3433,3505,3539,3637,3643,3665,3697,3739,3779,3817,3845,3877,3967,3985,4001,4013,4063,4151,4153,4195,4229,4271,4311,4327,4503,4543,4567,4573,4589,4633,4649,4663,4691,4717,4781,4811,4813,4841,4843,4855,4889}
奇数都可表为2的幂与一个素数之和
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直觉这样的奇数不会超过一半。猜测表示为两个2的幂之和加一个素数应该可以。 刚看到A006285 Odd numbers not of form p + 2^k (de Polignac numbers).
提到了
The upper asymptotic density of this sequence is smaller than 0.392352 不能表示为素数和平方数和的整数序列呢？
https://oeis.org/A020495
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