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A278735 Smallest prime-indexed prime ending an arithmetic progression of n prime-indexed primes.

%I A278735 #52 Jan 04 2017 06:54:30
%S A278735 3,5,17,587,47857,7336423,785979097
%N A278735 Smallest prime-indexed prime ending an arithmetic progression of n prime-indexed primes.
%C A278735 The first set of 4 prime-indexed primes in arithmetic progression (353, 431, 509, and 587) contains consecutive terms of A142160.
%e A278735 a(4) = 587 because 353 = prime(prime(20)), 431 = prime(prime(23)), 509 = prime(prime(25)), 587 = prime(prime(28)), and 431-353 = 509-431 = 587-509 = 78.
%e A278735 From _Charles R Greathouse IV_, Nov 27 2016: (Start)
%e A278735 The corresponding arithmetic progressions are
%e A278735 3;
%e A278735 3, 5;
%e A278735 5, 11, 17;
%e A278735 353, 431, 509, 587;
%e A278735 13297, 21937, 30577, 39217, 47857;
%e A278735 1561423, 2716423, 3871423, 5026423, 6181423, 7336423;
%e A278735 and with the main diagonal being terms of this sequence. (End)
%o A278735 (PARI) findAP(len)=my(t); if(len<3, return(v[len])); for(i=len, #v, for(j=1, i-len+1, t=(v[i]-v[j])/(len-1); if(denominator(t)>1, next); forstep(k=v[j]+t, v[i]-t, t, if(!setsearch(v, k), next(2))); return(vector(len, k, v[j]+(k-1)*t)))); "not found"
%o A278735 listPIP(lim)=my(v=List(), p); forprime(q=2, lim, if(isprime(p++), listput(v, q))); Vec(v)
%o A278735 v=listPIP(1e7);
%o A278735 apply(findAP, [1..6]) \\ _Charles R Greathouse IV_, Nov 27 2016
%Y A278735 Right border of A279021.
%Y A278735 Cf. A005115, A006450, A142160, A274825, A279062.
%K A278735 nonn,hard,more
%O A278735 1,1
%A A278735 _Bobby Jacobs_, Nov 27 2016
%E A278735 a(7) from _Charles R Greathouse IV_, Dec 27 2016