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

1,2

Comments

According to Brouwers et al., Deshouillers et al. showed that the maximum term of this sequence is 210. A141341 is a subsequence.

Positive integers k such that, for each prime p with k/2 <= p <= k - 2, k - p is prime. - Charles R Greathouse IV, May 28 2017

Links

Table of n, a(n) for n=1..21.

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.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A061358, A141341.

Sequence in context: A008726 A302834 A022788 * A287642 A182419 A033060

Adjacent sequences: A141337 A141338 A141339 * A141341 A141342 A141343

Keyword

nonn,nice,fini,full

Author

Rick L. Shepherd, Jun 25 2008

Status

approved