

A174216


a(1)=15; for n>1, a(n) = the smallest number k >a(n1) such that 2*A174214(k)= 3*(k1).


6



15, 27, 63, 123, 279, 567, 1143, 2307, 4623, 9447, 18927, 38283, 77139, 154839, 309747, 620463, 1241823, 2483847, 4967739, 9935607, 19892547, 39785199
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OFFSET

1,1


COMMENTS

Theorem: If the sequence is infinite, then there exist infinitely many twin primes.
Conjecture. a(n+1)/a(n) tends to 2.


LINKS

Table of n, a(n) for n=1..22.
V. Shevelev, Theorems on twin primesdual case, arXiv:0912.4006 [math.GM], 20092014.


MAPLE

A174216 := proc(n) option remember ; if n =1 then 15 ; else for k from procname(n1)+1 do if 2*A173214(k) = 3*(k1) then return k; end if; end do ; end if; end proc: # R. J. Mathar, Mar 16 2010


MATHEMATICA

(* b = A174214 *) b[n_] := b[n] = Which[n==9, 14, CoprimeQ[b[n1], n1 (1)^n], b[n1]+1, True, 2n4]; a[n_] := a[n] = If[n==1, 15, For[k = a[n 1]+1, True, k++, If[2b[k] == 3(k1), Return[k]]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 22}] (* JeanFrançois Alcover, Feb 02 2016 *)


CROSSREFS

Cf. A174214, A174215, A166945, A167495.
Sequence in context: A274433 A227804 A087719 * A249874 A116070 A186074
Adjacent sequences: A174213 A174214 A174215 * A174217 A174218 A174219


KEYWORD

nonn,more


AUTHOR

Vladimir Shevelev, Mar 12 2010


EXTENSIONS

Terms from a(11) on corrected by R. J. Mathar, Mar 16 2010
I corrected the terms beginning with a(11) and added some new terms.  Vladimir Shevelev, Mar 27 2010
Terms from a(11) onwards were corrected according to independent calculations by R. Mathar, M. Alekseyev, M. Hasler and A. Heinz (SeqFan lists 30 Oct and 1 Nov 2010).  Vladimir Shevelev, Nov 02 2010


STATUS

approved



