OFFSET

1,1

COMMENTS

0, 1, and 2 satisfy this condition for all p, so this sequence starts at 3. The growth of this sequence is much more irregular than that of the companion sequence A306582.

EXAMPLE

a(n) modulo 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...

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

3 1, 0, 2, 4, 8, 10, 14, 16, 20, 26, 28, ...

4 0, 2, 1, 3, 7, 9, 13, 15, 19, 25, 27, ...

7 1, 2, 3, 0, 4, 6, 10, 12, 16, 22, 24, ...

8 0, 1, 2, 6, 3, 5, 9, 11, 15, 21, 23, ...

16 0, 2, 4, 5, 6, 10, 1, 3, 7, 13, 15, ...

157 1, 2, 3, 4, 8, 12, 13, 14, 4, 17, 29, ...

16957 1, 2, 3, 4, 5, 8, 9, 10, 17, 8, 0, ...

19231 1, 2, 4, 5, 8, 9, 13, 16, 20, 25, 20, ...

80942 0, 1, 3, 6, 7, 9, 12, 17, 18, 26, 30, ...

PROG

(PARI) isok(k, n) = {my(last = -1, cur); for (i=1, n, cur = -k % prime(i); if (cur <= last, return (0)); last = cur; ); return (1); }

a(n) = {my(k=3); while(!isok(k, n), k++); k; } \\ Michel Marcus, Jun 04 2019

(Python)

from sympy import prime

def A306612(n):

plist, x = [prime(i) for i in range(1, n+1)], 3

rlist = [-x % p for p in plist]

while True:

for i in range(n-1):

if rlist[i] >= rlist[i+1]:

break

else:

return x

for i in range(n):

rlist[i] = (rlist[i] - 1) % plist[i]

x += 1 # Chai Wah Wu, Jun 15 2019

CROSSREFS

KEYWORD

nonn,hard

AUTHOR

Charlie Neder, Jun 03 2019

EXTENSIONS

a(16)-a(19) from Daniel Suteu, Jun 04 2019

a(20)-a(25) from Giovanni Resta, Jun 16 2019

a(26)-a(27) from Bert Dobbelaere, Jun 22 2019

a(28)-a(30) from Bert Dobbelaere, Sep 04 2019

STATUS

approved