A390467 Smallest composite member of an arithmetic progression of length k >= 3 where all preceding terms are primes.

9, 15, 25, 27, 33, 35, 45, 49, 55, 63, 65, 77, 85, 87, 91, 95, 105, 115, 117, 119, 123, 125, 133, 143, 145, 153, 155, 161, 169, 175, 185, 187, 195, 203, 205, 207, 209, 215, 217, 221, 235, 243, 245, 247, 253, 259, 265, 275, 285, 287, 289, 295, 297, 299, 301, 305, 315, 319

Offset

1,1

Comments

The common difference d of the arithmetic progression must necessarily be even. All terms are necessarily odd.

Links

Table of n, a(n) for n=1..58.

Example

a(1) = 9: The progression is (3, 5, 7) with d = 2. The next term is 7 + 2 = 9, which is composite.
a(2) = 15: The progression is (3, 7, 11) with d = 4. The next term is 11 + 4 = 15, which is composite.
a(3) = 25: The progression is (7, 13, 19) with d = 6. The next term is 19 + 6 = 25, which is composite (5 * 5).
a(6) = 35: The progression is (5, 11, 17, 23, 29) with d = 6. The next term is 29 + 6 = 35, which is composite (5 * 7). Note that 5 * (6 + 1) = 35.

Prog

(PARI) isok(k) = if(k%2 && !isprime(k), forprime(p=2*k\3+1, k-1, if(isprime(2*p-k)&&isprime(3*p-2*k), return(k-p)))); 0 \\ Andrew Howroyd, Feb 07 2026

Crossrefs

Sequence in context: A172292 A075638 A145743 * A164384 A138193 A330947

Adjacent sequences: A390464 A390465 A390466 * A390468 A390469 A390470

Keyword

nonn

Author

César Martínez, Feb 06 2026

Status

approved