A141340 Positive integers n such that A061358(n) = #{primes p | n/2 <= p < n-1}.
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 24, 30, 36, 42, 48, 60, 90, 210
Offset: 1
Examples
For each prime 210/2 <= p <= 210, 210 - p is prime, and so 210 is in this sequence: 210 - 107 = 103, 210 - 109 = 101, 210 - 113 = 97, 210 - 127 = 83, 210 - 131 = 79, 210 - 137 = 73, 210 - 139 = 71, 210 - 149 = 61, 210 - 151 = 59, 210 - 157 = 53, 210 - 163 = 47, 210 - 167 = 43, 210 - 173 = 37, 210 - 179 = 31, 210 - 181 = 29, 210 - 191 = 19, 210 - 193 = 17, 210 - 197 = 13, 210 - 199 = 11. - _Charles R Greathouse IV_, May 28 2017
Links
- J-M. Deshouillers, A. Granville, W. Narkiewicz and C. Pomerance, An upper bound in Goldbach's problem, Math. Comp. 61 (1993), 209-213.
- Brady Haran and Carl Pomerance, 210 is VERY Goldbachy, Numberphile video (2017)
- David van Golstein Brouwers, John Bamberg and Grant Cairns, Totally Goldbach numbers and related conjectures, The Australian Mathematical Society, Gazette, Volume 31 Number 4, September 2004.
Programs
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Mathematica
Block[{r = {}}, Do[ If[ AllTrue[i - #, PrimeQ] &@ NextPrime[i/2, Range[ PrimePi[i - 2] - PrimePi[i/2]]], AppendTo[r, i]], {i, 210}]; r] (* Mikk Heidemaa, May 29 2024 *) -
PARI
is(n)=forprime(p=n/2,n-2, if(!isprime(n-p),return(0))); 1 \\ Charles R Greathouse IV, May 28 2017; corrected by Michel Marcus, May 30 2024
Comments