A008601 -id:A008601 - cp's OEIS frontend

A144619 a(n) = 19*n + 8.

8, 27, 46, 65, 84, 103, 122, 141, 160, 179, 198, 217, 236, 255, 274, 293, 312, 331, 350, 369, 388, 407, 426, 445, 464, 483, 502, 521, 540, 559, 578, 597, 616, 635, 654, 673, 692, 711, 730, 749, 768, 787, 806, 825, 844, 863, 882, 901, 920, 939, 958, 977, 996

Offset: 0

Vincenzo Librandi, Jan 15 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008601, A141873, A144620.

I:=[8, 27]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // Vincenzo Librandi, May 14 2012

Range[8, 1500, 19] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
CoefficientList[Series[(8+11*x)/(x-1)^2,{x,0,60}],x] (* Vincenzo Librandi, May 14 2012 *)
LinearRecurrence[{2,-1},{8,27},60] (* Harvey P. Dale, Jun 17 2020 *)

From Vincenzo Librandi, May 14 2012: (Start)
G.f.: (11*x+8)/(1-x)^2.
a(n) = 2*a(n-1) - a(n-2). (End)
E.g.f.: exp(x)*(8 + 19*x). - Elmo R. Oliveira, Apr 04 2025

Offset corrected by Jon E. Schoenfield, Jun 17 2010

A138129 Multiples of 1729, the Hardy-Ramanujan number.

Original entry on oeis.org

0, 1729, 3458, 5187, 6916, 8645, 10374, 12103, 13832, 15561, 17290, 19019, 20748, 22477, 24206, 25935, 27664, 29393, 31122, 32851, 34580, 36309, 38038, 39767, 41496, 43225, 44954, 46683, 48412, 50141, 51870, 53599, 55328, 57057, 58786, 60515, 62244, 63973, 65702, 67431

Offset: 0

Omar E. Pol, Mar 09 2008

About 1729: "No," said Ramanujan, "It is a very interesting number..."

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1997, p. 153.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A001235, A011541, A133019, A133029, A138130.

Cf. A008601.

1729Range[0, 37] (* Alonso del Arte, Feb 19 2015 *)

a(n)=1729*n \\ Charles R Greathouse IV, Feb 21 2015

concat(0, Vec(1729*x/(1-x)^2 + O(x^40))) \\ Elmo R. Oliveira, Jun 23 2025

a(n) = 1729*n.
From Elmo R. Oliveira, Jun 23 2025: (Start)
G.f.: 1729*x/(1-x)^2.
E.g.f.: 1729*x*exp(x).
a(n) = 91*A008601(n).
a(n) = 2*a(n-1) - a(n-2). (End)

More terms from Elmo R. Oliveira, Jun 23 2025

A166392 Multiples of 19 whose reversal + 1 is also a multiple of 19.

Original entry on oeis.org

57, 570, 722, 893, 1254, 1406, 1577, 1729, 2641, 2964, 3097, 3249, 4161, 4313, 4484, 4636, 4959, 5700, 5871, 6156, 6308, 6479, 7220, 7391, 7543, 7866, 8930, 9063, 9215, 9386, 9538

Offset: 1

Claudio Meller, Oct 13 2009

G. C. Greubel, Table of n, a(n) for n = 1..10000

Subsequence of A008601.

Select[19 Range[5!], Divisible[FromDigits[Reverse[IntegerDigits[#]]] + 1, 19] &](* G. C. Greubel, May 12 2016 *)

A166399 Multiples of 19 whose digit reversal - 1 is also a multiple of 19.

Original entry on oeis.org

247, 1083, 1235, 1558, 2470, 2622, 2793, 2945, 3078, 4142, 4465, 4617, 4788, 5852, 6137, 7201, 7372, 7524, 7695, 7847, 8911, 9044, 9367, 9519, 10830, 11115, 11286, 11438, 12350, 12502, 12673, 12825, 12996, 14022, 14193, 14345, 14668, 15580, 15732

Offset: 1

Claudio Meller, Oct 13 2009

G. C. Greubel, Table of n, a(n) for n = 1..10000

Subsequence of A008601.

Select[19 Range[5!], Divisible[FromDigits[Reverse[IntegerDigits[#]]] - 1, 19] &] (* G. C. Greubel, May 12 2016 *)

Keyword:base added by R. J. Mathar, Oct 16 2009

A377030 Period 19: repeat [0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3].

Original entry on oeis.org

0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3, 0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3, 0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3, 0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3, 0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3, 0

Offset: 0

Neil Vaughan, Oct 13 2024

Difference between the multiples of 3 (A008585) and the closest multiple of 19 (A008601). For any two numbers (in this case p=3 and q=19), a sequence is produced consisting of a palindrome cycle. If p and q are coprime, then the cycle length is equal to max(p,q). The biggest number in the sequence will be at most half of max(p,q). Here is a plot of the first cycle of this sequence:
     X                          X
                  X X
       X                      X
   X                              X
               X      X
         X                  X
 X                                  X
             X          X
           X              X
X                                      X

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A008585, A008601.

int p = 3;
int q = 19;
for (int t = 0;t <= 99;t++) {
	int closest = 999;
	for (int i = 0;i <= 99;i++) {
		int dist=abs(i * q - t * p);
		if (dist < closest) {
			closest = dist;
		}
	}
	printf("%i, ", closest);
}

LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},{0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3},96] (* James C. McMahon, Oct 31 2024 *)

a(n) = my(n3 = 3*n); min(n3 - 19*floor(n3/19), ceil(19*ceil(n3/19) - n3)) \\ David A. Corneth, Oct 14 2024

def A377030(n): return (0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3)[n%19] # Chai Wah Wu, Oct 31 2024

a(n) = a(n-19). - David A. Corneth, Oct 14 2024

a(n) = min(3*n-19*floor(3*n/19), 19*ceil(3*n/19)-3*n).

cp's OEIS Frontend

A144619 a(n) = 19*n + 8.

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A138129 Multiples of 1729, the Hardy-Ramanujan number.

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A166392 Multiples of 19 whose reversal + 1 is also a multiple of 19.

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A166399 Multiples of 19 whose digit reversal - 1 is also a multiple of 19.

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A377030 Period 19: repeat [0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3].

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