



3, 7, 11, 23, 17, 37, 23, 41, 43, 61, 47, 61, 53, 73, 109, 107, 89, 73, 109, 227, 113, 113, 139, 157, 127, 149, 127, 131, 283, 137, 139, 181, 173, 179, 167, 191, 181, 227, 193, 251, 239, 199, 233, 257, 239, 251, 239, 241, 271, 313, 241, 271, 281, 277, 443, 389
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

a(n) < (prime(n))^3 yields an infinity of twin primes (it is sufficient, if this inequality holds for an arbitrary infinite subsequence n = n_k). For a proof, see the Shevelev link (Remark 8).
The author apparently claims to have proved the infinitude of twin primes. No alleged proof has been accepted by the mathematical community.  Jens Kruse Andersen, Jul 13 2014
In the statistical part of my link (Section 14), using the Chinese Remainder and Tolev's theorems, I reduced the supposition of the finiteness of twin primes to an arbitrarily long coinflipping experiment in which only "heads" appear. There I gave only a "demonstration" of the infinity of twin primes. In the analytical part (Sections 1518) I proved unconditionally till now only Theorem 13.  Vladimir Shevelev, Jul 22 2014


LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 2..10000
V. Shevelev, Theorems on twin primesdual case, arXiv:0912.4006 [math.GM], 20102014. (Sections 10,1418). [Note this article has been changed many times.]


MATHEMATICA

a[n_, k_] := For[p = Prime[n], True, p = NextPrime[p], If[PrimeQ[p Prime[n] + k], Return[p]]];
a[n_] := Max[a[n, 2], a[n, 2]];
Table[a[n], {n, 2, 60}] (* JeanFrançois Alcover, Nov 18 2018 *)


CROSSREFS

Cf. A244570, A244571, A242519, A242520.
Sequence in context: A082675 A201645 A028831 * A137516 A247380 A187265
Adjacent sequences: A244569 A244570 A244571 * A244573 A244574 A244575


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Jun 30 2014


EXTENSIONS

More terms from Peter J. C. Moses, Jun 30 2014


STATUS

approved



