A328298 The smaller prime in the decomposition of 2n (>=6) into a sum of two odd primes obtained from increasing the smaller prime of such a decomposition of 2n-2.

3, 3, 5, 5, 7, 5, 7, 7, 11, 11, 13, 11, 13, 13, 17, 17, 19, 17, 19, 13, 17, 19, 19, 23, 23, 19, 29, 29, 31, 23, 29, 31, 29, 31, 37, 29, 31, 37, 41, 41, 43, 41, 43, 31, 41, 43, 37, 41, 43, 43, 47, 47, 43, 53, 53, 43, 47, 53, 61, 53, 59, 61, 59, 61, 67, 53, 59

Offset

3,1

Comments

This sequence is different from A002374 from the 23rd term on.

Links

Table of n, a(n) for n=3..69.

Example

For the 3rd even number 6, 6=3+3;
For the 4th number 8, increasing the first prime in 6=3+3 by 2, we get 8=5+3, 5 and 3 are both primes, choose the smaller one, the second term of this sequence is 3, which makes 8=3+5;
...
For the 23rd even number 46, increasing the first prime in 44=13+31 by 2, we get 46=15+31.  15 is not prime, keep increasing: 46=17+29.  Both 17 and 29 are primes, so the 23rd term of this sequence is 17, as of 46=17+29;
...
For 28th even number 56, increasing the first prime in 54=23+31 by 2, we get 56=25+31.  25 is not prime, keep increasing, 56 = 27+29 = 29+27 = 31+25 = 33+23 = 35+21 = 37+19.  Both 37 and 19 are primes, and 19 is smaller.  So the 28th term of this sequence is 19, as of 56=19+37.

Mathematica

e = 4; p1 = 1; p2 = 3; a = Table[e = e + 2; If[p1 < p2, p1 = p1 + 2, p2 = p2 + 2];
  While[! (PrimeQ[p1] && PrimeQ[p2]), p1 = p1 + 2; p2 = p2 - 2];
  If[p1 > p2, p1 = p2; p2 = e - p1]; p1, {i, 1, 67}]

Crossrefs

Cf. A002374, A112823.

Sequence in context: A021302 A004649 A367004 * A002374 A261046 A226482

Adjacent sequences: A328295 A328296 A328297 * A328299 A328300 A328301

Keyword

easy,nonn

Author

Lei Zhou, Oct 11 2019

Status

approved