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 A306582 a(n) is the least integer k such that the remainder of k modulo p is strictly increasing over the first n primes. 5
 0, 2, 4, 34, 52, 194, 502, 1138, 4042, 5794, 5794, 62488, 798298, 5314448, 41592688, 483815692, 483815692, 5037219688, 18517814158, 18517814158, 19566774820732, 55249201504132, 1257253598786974, 6743244322196288, 24165921989926702, 24165921989926702, 5346711077171356252, 47449991406350138602, 278545375679341352084, 5604477496256287791854 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If "strictly increasing" is replaced with "nondecreasing", this sequence becomes A000004. Trivially, a(n) <= A002110(n)-2. Equality only holds for n = 0. LINKS EXAMPLE a(n) modulo 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...   ==== ==================================================      0        0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0, ...      2        0, 2, 2, 2,  2,  2,  2,  2,  2,  2,  2, ...      4        0, 1, 4, 4,  4,  4,  4,  4,  4,  4,  4, ...     34        0, 1, 4, 6,  1,  8,  0, 15, 11,  5,  3, ...     52        0, 1, 2, 3,  8,  0,  1, 14,  6, 23, 21, ...    194        0, 2, 4, 5,  7, 12,  7,  4, 10, 20,  8, ...    502        0, 1, 2, 5,  7,  8,  9,  8, 19,  9,  6, ...   1138        0, 1, 3, 4,  5,  7, 16, 17, 11,  7, 22, ...   4042        0, 1, 2, 3,  5, 12, 13, 14, 17, 11, 12, ...   5794        0, 1, 4, 5,  8,  9, 14, 18, 21, 23, 28, ... 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=0); while(!isok(k, n), k++); k; } \\ Michel Marcus, Jun 04 2019 (Python) from sympy import prime def A306582(n):     plist, rlist, x = [prime(i) for i in range(1, n+1)], [0]*n, 0     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 Cf. A000004, A002110, A306612, A325057. Sequence in context: A178811 A099433 A051225 * A103625 A006989 A236399 Adjacent sequences:  A306579 A306580 A306581 * A306583 A306584 A306585 KEYWORD nonn,hard AUTHOR Charlie Neder, Jun 03 2019 EXTENSIONS a(16)-a(20) from Daniel Suteu, Jun 03 2019 a(21)-a(23) from Giovanni Resta, Jun 16 2019 a(24)-a(27) from Bert Dobbelaere, Jun 22 2019 a(28)-a(30) from Bert Dobbelaere, Sep 05 2019 STATUS approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)