

A100366


a(n) is the least prime number q such that q,q+1,q+2,q+3,...,q+n1 have 2,4,8,...,2^n divisors respectively.


1




OFFSET

1,1


COMMENTS

a(3), a(4), a(5) are the initial terms of A100363, A100364, A100365 resp.
Any run of 8 or more consecutive integers must include at least one number k of the form 8j+4; in the prime factorization of k, the prime factor 2 appears with multiplicity exactly 2, so the number of divisors of k is divisible by 3 (which is not a power of 2). Thus, there is no term a(8): the sequence is complete, ending with a(7).  Jon E. Schoenfield, Nov 12 2017


LINKS

Table of n, a(n) for n=1..7.


EXAMPLE

a(4)=613: q=613 (a prime, hence two divisors), q+1 = 614 = 2*307 (4 divisors), q+2 = 615 = 3*5*41 (8 divisors), and q+3 = 616 = 2^3 * 7 * 11 (16 divisors).


CROSSREFS

Cf. A000005, A063446, A100363, A100364.
Sequence in context: A111392 A226071 A319143 * A012975 A012954 A006271
Adjacent sequences: A100363 A100364 A100365 * A100367 A100368 A100369


KEYWORD

nonn,fini,full


AUTHOR

Labos Elemer, Nov 19 2004


EXTENSIONS

a(6)a(7) from Donovan Johnson, Mar 23 2011
Keywords fini and full added and Example section edited by Jon E. Schoenfield, Nov 12 2017


STATUS

approved



