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A100366 a(n) is the least prime number q such that q,q+1,q+2,q+3,...,q+n-1 have 2,4,8,...,2^n divisors respectively. 1
2, 5, 193, 613, 1124581, 52071301, 213536830501 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 4 07:59 EDT 2020. Contains 334822 sequences. (Running on oeis4.)