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 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-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

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Last modified December 8 04:55 EST 2023. Contains 367662 sequences. (Running on oeis4.)