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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). 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 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

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