A278588
Triangle read by rows: T(p_1,p_2) = maximal period of a decimal fraction (r/s)*(t/u) given that r/s has period p_1 and t/u has period p_2 (1 <= p_1 <= p_2).
Original entry on oeis.org
9, 18, 198, 27, 54, 2997, 36, 396, 108, 39996, 45, 90, 135, 180, 499995, 54, 594, 5994, 3564, 270, 5999994, 63, 126, 189, 252, 315
Offset: 1
Triangle begins (read down columns):
...1.....2....3....4....5.....6......7....(p_2)
1..9....18...27...36...45....54.....63
2......198...54..396...90...594....126
3..........2997..108..135..5994....189
4..............39996..180..3564....252
5..................499995...270....315
...
(p_1)
A328683
Positive integers that are equal to 99...99 (repdigit with n digits 9) times the sum of their digits.
Original entry on oeis.org
81, 1782, 26973, 359964, 4499955, 53999946, 629999937, 7199999928, 80999999919, 899999999910, 9899999999901, 107999999999892, 1169999999999883, 12599999999999874, 134999999999999865, 1439999999999999856, 15299999999999999847, 161999999999999999838
Offset: 1
359964 = 36 * 9999 and the digital sum of 359964 = 36 , so 359964 = a(4).
- Roman Fedorov, Alexei Belov, Alexander Kovaldzhi, Ivan Yashchenko, Moscow Mathematical Olympiads, 2000-2005, Level B, Problem 5, 2001, MSRI, 2011, p. 8 and 70/71.
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C:=seq(9*n*(10^n-1),n=1..20);
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Table[9*n*(10^n - 1), {n, 1, 18}] (* Amiram Eldar, Feb 25 2020 *)
LinearRecurrence[{22,-141,220,-100},{81,1782,26973,359964},20] (* Harvey P. Dale, Feb 02 2025 *)
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Vec(81*x*(1 - 10*x^2) / ((1 - x)^2*(1 - 10*x)^2) + O(x^20)) \\ Colin Barker, Feb 25 2020
A109137
Numbers k such that k * (10^k - 1) + 1 is prime.
Original entry on oeis.org
2, 14, 42, 144, 200, 302, 7242, 8718, 10568, 24438, 41734
Offset: 1
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is(n)=ispseudoprime(n*(10^n-1)+1) \\ Charles R Greathouse IV, Jun 13 2017
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from sympy import isprime
def afind(limit, startk=1):
k, pow10 = startk, 10**startk
for k in range(startk, limit+1):
if isprime(k*(pow10 - 1) + 1): print(k, end=", ")
k += 1
pow10 *= 10
afind(500) # Michael S. Branicky, Aug 26 2021
Showing 1-3 of 3 results.
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