A352338 Prime numbers of the form (i+1)*A352185(i) + A352186(i) for some i > 0.

7, 19, 29, 71, 103, 191, 577, 967, 1511, 3697, 4793, 7121, 9371, 13033, 17401, 24107, 37363, 134371, 165523, 220301, 307651, 503771, 735181, 1029349, 1119403, 1348387, 2148893, 4012709, 6188401, 7379387, 7928527, 8352037, 9819037, 10880687, 13261627, 19005359

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..36.

Richard K. Guy, What are the smallest arithmetic progressions of composite numbers?, Amer. Math. Monthly, Vol. 93, No. 8 (1986), p. 627.

Rémy Sigrist, C++ program

Example

For i = 33:
- A352185(33) = 139 < A352185(34) = 193,
- (33+1) * A352185(33) + A352186(33) = 34 * 139 + 67 = 4793,
- so 4793 belongs to this sequence.

Prog

(C++) See Links section.

Crossrefs

Cf. A352185, A352186.

Sequence in context: A117609 A122072 A261338 * A109355 A272404 A274971

Adjacent sequences: A352335 A352336 A352337 * A352339 A352340 A352341

Keyword

nonn

Author

Rémy Sigrist, Mar 13 2022

Status

approved