A025019 Smallest prime in Goldbach partition of A025018(n).

2, 3, 5, 7, 19, 23, 31, 47, 73, 103, 139, 173, 211, 233, 293, 313, 331, 359, 383, 389, 523, 601, 727, 751, 829, 929, 997, 1039, 1093, 1163, 1321, 1427, 1583, 1789, 1861, 1877, 1879, 2029, 2089, 2803, 3061, 3163, 3457, 3463, 3529, 3613, 3769, 3917, 4003, 4027, 4057

Offset: 1

Author

David W. Wilson, Dec 11 1999

Keywords

• nonn

Comments

Increasing subsequence of A020481.

For n > 2, a(n) ~ (log(A025018(n)))^e/e, while an upper bound could be written as UB(a(n)) = floor(log(A025018(n)))^e/2 (therefore, for any even v such that 12 <= v <= A025018(67) UB is true). It looks that both approximation and UB are true for any n > 2. Assuming the second equation to be true, UB(10^80) = 718967, UB(10^500) = 104745517, etc. - Sergey Pavlov, Jan 17 2021

Examples

			1427 and 1583 are two consecutive terms because A020481(167535419) = 1427 and A020481(209955962) = 1583 and for 167535419 < n < 209955962 A020481(n) <= 1427.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n=1..67 (from the web page of Tomás Oliveira e Silva)
• Mark A. Herkommer, Goldbach Conjecture Research
• Tomás Oliveira e Silva, Goldbach conjecture verification
• Jörg Richstein, Verifying the Goldbach conjecture up to 4 * 10^14, Math. Comp., 70 (2001), 1745-1749.
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A025018, A020481, A097224, A097226.

Programs

Mathematica

p = 1; q = {}; Do[ k = 2; While[ !PrimeQ[k] || !PrimeQ[2n - k], k++ ]; If[k > p, p = k; q = Append[q, p]], {n, 2, 10^8}]; q

Extensions

Edited and extended by Robert G. Wilson v, Dec 13 2002

More terms and b-file added by N. J. A. Sloane, Nov 28 2007