A174216 - OEIS

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A174216

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

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 primes-dual case, arXiv:0912.4006 [math.GM], 2009-2014.

MAPLE

A174216 := proc(n) option remember ; if n =1 then 15 ; else for k from procname(n-1)+1 do if 2*A173214(k) = 3*(k-1) 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[n-1], n-1- (-1)^n], b[n-1]+1, True, 2n-4]; a[n_] := a[n] = If[n==1, 15, For[k = a[n- 1]+1, True, k++, If[2b[k] == 3(k-1), Return[k]]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 22}] (* Jean-François Alcover, Feb 02 2016 *)

CROSSREFS

Cf. A174214, A174215, A166945, A167495.

Sequence in context: A365451 A343139 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