A352186 The numbers k arising in A352185.

1, 4, 1, 5, 5, 12, 1, 1, 1, 19, 19, 19, 19, 19, 19, 19, 19, 27, 27, 47, 47, 47, 47, 14, 14, 14, 14, 14, 67, 67, 67, 67, 67, 173, 173, 211, 211, 211, 211, 15, 15, 15, 15, 15, 15, 214, 214, 214, 214, 214, 385, 385, 385, 385, 385, 385, 385, 22, 22, 22, 22, 22, 22, 22

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..232

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

Prog

(Python)
from math import gcd
from sympy import isprime
from itertools import count, islice, takewhile
def comp(n): return not isprime(n)
def agen(): # generator of terms
    n = 1
    for m in count(2):
        for k in range(1, m):
            if gcd(k, m) != 1:
                continue
            ap = len(list(takewhile(comp, (i*m+k for i in count(1)))))
            if ap >= n:
                for i in range(n, ap+1):
                    yield k
                n = ap + 1
print(list(islice(agen(), 64)))  # Michael S. Branicky, Mar 12 2022

Crossrefs

Cf. A352185.

Sequence in context: A075013 A117379 A007309 * A333341 A344027 A084890

Adjacent sequences: A352183 A352184 A352185 * A352187 A352188 A352189

Keyword

nonn

Author

N. J. A. Sloane, Mar 12 2022

Extensions

a(24) and beyond from Michael S. Branicky, Mar 12 2022.

Status

approved