login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 21 2020, after Maple *)

CROSSREFS

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

Sequence in context: A045316 A040100 A076757 * A045404 A152460 A130097

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 13:25 EDT 2021. Contains 343204 sequences. (Running on oeis4.)