login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325057 Number of positive integers k < prime(n)# so that (k mod p_1) < (k mod p_2) < ... < (k mod p_n). 2
2, 3, 7, 19, 94, 381, 2217, 10248, 64082, 572741, 3590815, 33731134, 291308123, 1896596488, 14675287694, 147847569839, 1642854121867, 12717640104203, 134707566446733, 1285768348848054, 9334472487460317, 97284913917125312, 922382339920122509, 10370484766702974615 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence emerges during computation of A306582 and A306612.

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

a(3) = 7:

Solutions for k that have increasing remainders modulo the first 3 primes:

k   modulo  2   3   5

=====================

22          0 < 1 < 2

28          0 < 1 < 3

4           0 < 1 < 4

8           0 < 2 < 3

14          0 < 2 < 4

23          1 < 2 < 3

29          1 < 2 < 4

PROG

(Python)

from sympy import prime

def f(k, r, n):

....if k==n: return prime(k)-r

....global cache ; args = (k, r)

....if args in cache: return cache[args]

....rv = f(k+1, r+1, n)

....if r < (prime(k)-1): rv += f(k, r+1, n)

....cache[args]=rv ; return rv

def A325057(n):

....global cache ; cache = {}

....return f(1, 0, n)

CROSSREFS

Cf. A002110, A306582, A306612.

Sequence in context: A164625 A294148 A079804 * A075487 A110498 A244917

Adjacent sequences:  A325054 A325055 A325056 * A325058 A325059 A325060

KEYWORD

nonn

AUTHOR

Bert Dobbelaere, Sep 04 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 20:49 EST 2021. Contains 349395 sequences. (Running on oeis4.)