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Initial terms of the arithmetic progressions in A278735.
3

%I #33 Jan 04 2017 07:00:35

%S 3,3,5,353,13297,1561423,291461857

%N Initial terms of the arithmetic progressions in A278735.

%C The first set of 4 prime-indexed primes in arithmetic progression (353, 431, 509, and 587) contains consecutive terms of A142160.

%e a(4) = 353 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 The corresponding arithmetic progressions are

%e 3;

%e 3, 5;

%e 5, 11, 17;

%e 353, 431, 509, 587;

%e 13297, 21937, 30577, 39217, 47857;

%e 1561423, 2716423, 3871423, 5026423, 6181423, 7336423;

%e ...

%Y Left border of A279021.

%Y Cf. A006450, A113827, A142160, A274825, A278735.

%K nonn,hard,more

%O 1,1

%A _Bobby Jacobs_, Dec 05 2016

%E a(7) from _Charles R Greathouse IV_, Dec 27 2016