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A325057
Number of positive integers k <= prime(n)# so that (k mod p_1) < (k mod p_2) < ... < (k mod p_n).
3
1, 2, 3, 7, 19, 94, 381, 2217, 10248, 64082, 572741, 3590815, 33731134, 291308123, 1896596488, 14675287694, 147847569839, 1642854121867, 12717640104203, 134707566446733, 1285768348848054, 9334472487460317, 97284913917125312, 922382339920122509, 10370484766702974615
OFFSET
0,2
COMMENTS
This sequence emerges during computation of A306582 and A306612.
LINKS
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
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
add(b(n-1, j-1), j=1..min(i, ithprime(n))))
end:
a:= n-> b(n, infinity):
seq(a(n), n=0..24); # Alois P. Heinz, Jan 04 2023
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
KEYWORD
nonn
AUTHOR
Bert Dobbelaere, Sep 04 2019
EXTENSIONS
Name edited and a(0)=1 prepended by Alois P. Heinz, Jan 04 2023
STATUS
approved