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Prime numbers of the form (i+1)*A352185(i) + A352186(i) for some i > 0.
1

%I #14 Mar 30 2023 15:14:48

%S 7,19,29,71,103,191,577,967,1511,3697,4793,7121,9371,13033,17401,

%T 24107,37363,134371,165523,220301,307651,503771,735181,1029349,

%U 1119403,1348387,2148893,4012709,6188401,7379387,7928527,8352037,9819037,10880687,13261627,19005359

%N Prime numbers of the form (i+1)*A352185(i) + A352186(i) for some i > 0.

%C These prime numbers end the arithmetic progressions of composite numbers introduced in A352185-A352186.

%C The values for i are those where A352185(i) < A352185(i+1).

%H Richard K. Guy, <a href="http://www.jstor.org/stable/2322320">What are the smallest arithmetic progressions of composite numbers?</a>, Amer. Math. Monthly, Vol. 93, No. 8 (1986), p. 627.

%H Rémy Sigrist, <a href="/A352338/a352338.txt">C++ program</a>

%e For i = 33:

%e - A352185(33) = 139 < A352185(34) = 193,

%e - (33+1) * A352185(33) + A352186(33) = 34 * 139 + 67 = 4793,

%e - so 4793 belongs to this sequence.

%o (C++) See Links section.

%Y Cf. A352185, A352186.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Mar 13 2022