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A078497 The member r of a triple of primes (p,q,r) in arithmetic progression which sum to 3*prime(n) = A001748(n) = p + q + r.

%I A078497 #8 Aug 07 2015 02:37:28
%S A078497 7,11,17,19,23,31,29,41,43,43,53,67,53,59,71,79,73,83,79,97,107,107,
%T A078497 127,113,109,113,139,137,151,149,167,151,167,163,163,199,197,179,191,
%U A078497 199,233,223,227,241,223,283,257,277,239,251,271,263,263,269,281,313
%N A078497 The member r of a triple of primes (p,q,r) in arithmetic progression which sum to 3*prime(n) = A001748(n) = p + q + r.
%C A078497 In case more than one triple of primes p, q=p+d and r=p+2*d exists, we take r=a(n) from the triple with the smallest d. This shows the difference from A092940, which would take the maximum r over all triples. - _R. J. Mathar_, May 19 2007
%e A078497 a(1) = 7 because 3+5+7 = 15;
%e A078497 a(2) = 11 because 3+7+11 = 21;
%e A078497 a(3) = 17 because 5+11+17= 33.
%p A078497 A078497 := proc(n) local p3, i,d,r,p; p3 := ithprime(n) ; i := n+1 ; while true do r := ithprime(i) ; d := r-p3 ; p := p3-d ; if isprime(p) then RETURN(r) ; fi ; i := i+1 ; od ; RETURN(-1) ; end: for n from 3 to 60 do printf("%d, ",A078497(n)) ; od ; # _R. J. Mathar_, May 19 2007
%t A078497 f[n_] := Block[{p = Prime[n], k}, k = p + 1; While[ !PrimeQ[k] || !PrimeQ[2p - k], k++ ]; k]; Table[ f[n], {n, 3, 60}]
%Y A078497 Cf. A078496, A078498, A001748, A092940, A071681, A078611.
%K A078497 nonn
%O A078497 3,1
%A A078497 Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), Nov 27 2002
%E A078497 Edited and extended by _Robert G. Wilson v_, Nov 29 2002
%E A078497 Further edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_