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A284708 Smallest initial prime p for at least n primes in increasing arithmetic progression with a common difference less than p.

%I A284708 #40 Mar 16 2023 11:25:11
%S A284708 2,2,3,11,37,107,409,409,409,25471,53173,65003,766439,11797483
%N A284708 Smallest initial prime p for at least n primes in increasing arithmetic progression with a common difference less than p.
%C A284708 Conjecture: a(n) > A034386(n) for every n >= 4.
%C A284708 From _Bernard Schott_, Mar 15 2023: (Start)
%C A284708 Corresponding common differences are in A361492.
%C A284708 a(22) = 11410337850553 since it is the smallest term in a sequence of 22 primes in arithmetic progression, and the corresponding common difference 4609098694200 is < a(22) (see Penguin reference). (End)
%D A284708 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, entry 11410337850553, page 191.
%e A284708 Smallest initial prime p, primes in arithmetic progression:
%e A284708 a(1) = 2: (2);
%e A284708 a(2) = 2: (2, 3);
%e A284708 a(3) = 3: (3, 5, 7);
%e A284708 a(4) = 11: (11, 17, 23, 29);
%e A284708 a(5) = 37: (37, 67, 97, 127, 157);
%e A284708 a(6) = 107: (107, 137, 167, 197, 227, 257);
%e A284708 a(7) = 409: (409, 619, 829, 1039, 1249, 1459, 1669);
%e A284708 a(8) = 409: (409, 619, 829, 1039, 1249, 1459, 1669, 1879);
%e A284708 a(9) = 409: (409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089);
%o A284708 (PARI) isokd(p, n, d) = for (i=1, n, if (!isprime(p+(i-1)*d), return(0))); 1;
%o A284708 isokp(p, n) = for (d=1, p-1, if (isokd(p, n, d), return(1)););
%o A284708 a(n) = my(p=2); while (!isokp(p, n), p=nextprime(p+1)); p; \\ _Michel Marcus_, Mar 15 2023
%Y A284708 Cf. A361492.
%Y A284708 Cf. A123556, A342309.
%K A284708 nonn,more
%O A284708 1,1
%A A284708 _Arkadiusz Wesolowski_, Jan 09 2018
%E A284708 Name edited by _Bernard Schott_, Mar 15 2023