A078497 - OEIS

%I #8 Aug 07 2015 02:37:28

%S 7,11,17,19,23,31,29,41,43,43,53,67,53,59,71,79,73,83,79,97,107,107,

%T 127,113,109,113,139,137,151,149,167,151,167,163,163,199,197,179,191,

%U 199,233,223,227,241,223,283,257,277,239,251,271,263,263,269,281,313

%N 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 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 a(1) = 7 because 3+5+7 = 15;

%e a(2) = 11 because 3+7+11 = 21;

%e a(3) = 17 because 5+11+17= 33.

%p 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 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 Cf. A078496, A078498, A001748, A092940, A071681, A078611.

%K nonn

%O 3,1

%A Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), Nov 27 2002

%E Edited and extended by _Robert G. Wilson v_, Nov 29 2002

%E Further edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_