A178942 a(1) = 3; for n >= 2, a(n) is the smallest prime q > a(n-1) such that, for the previous prime p and the following prime r, the fraction (q-p)/(r-q) has denominator equal to A001223(n)/2 (or 0, if no such prime exists).

3, 5, 11, 13, 17, 19, 29, 37, 47, 53, 61, 67, 71, 79, 83, 131, 137, 151, 163, 173, 233, 277, 331, 359, 379, 397, 401, 419, 439, 773, 823, 941, 947, 1021, 1031, 1033, 1063, 1087, 1097, 1117, 1123, 1153, 1187, 1237, 1277, 1709, 1789, 1823

Offset

1,1

Comments

Conjecture: a(n) > 0 for all n.

The smallest prime(k) > a(n-1) such that the denominator of A001223(k-1)/A001223(k) equals A001223(n)/2. - R. J. Mathar, Jan 07 2011

Links

Table of n, a(n) for n=1..48.

Maple

A001223 := proc(n) ithprime(n+1)-ithprime(n) ; end proc:
A178942 := proc(n) option remember; local p, q, r ; if n = 1 then 3; else for q from procname(n-1)+1 do if isprime(q) then p := prevprime(q) ; r := nextprime(q) ; denom((q-p)/(r-q)) ; if % = A001223(n)/2 then return q; end if; end if; end do: end if; end proc: # R. J. Mathar, Jan 07 2011

Mathematica

A001223[n_] := Prime[n + 1] - Prime[n];
a[n_] := a[n] = Module[{p, q, r, d}, If[n == 1, 3, For[q = a[n - 1] + 1, True, q++, If [PrimeQ[q], p = NextPrime[q, -1]; r = NextPrime[q]; d = Denominator[(q - p)/(r - q)]; If[d == A001223[n]/2, Return[q]]]]]];
Array[a, 48] (* Jean-François Alcover, May 21 2020, after Maple *)

Crossrefs

Cf. A001223, A168253, A179210, A179234, A179240, A179328.

Sequence in context: A045316 A040100 A076757 * A045404 A154500 A152460

Adjacent sequences: A178939 A178940 A178941 * A178943 A178944 A178945

Keyword

nonn

Author

Vladimir Shevelev, Jan 06 2011

Extensions

More terms from Alois P. Heinz, Jan 06 2011

Status

approved