Chris Cole - cp's OEIS frontend

A166736 Consider triangles stacked so the k-th row has 2*k-1 triangles. a(n) is the number of ways to color each triangle in the first n rows using three colors with the restriction that adjacent triangles must be different colors. (Triangles are adjacent if they share a side.)

3, 24, 528, 31968, 5332224, 2450774016, 3104112826368

Offset: 1

Chris Cole (chris(AT)questrel.com), Oct 20 2009

nonn

			Illustration of first two rows:
           /\
          /  \
         /  1 \
        /      \
       /________\
      /\        /\
     /  \      /  \
    /  2 \  3 /  4 \
   /      \  /      \
  /________\/________\
Triangles sharing a side are considered adjacent; e.g., 1 & 3 are adjacent in the figure, 1 & 2 are not.

Project Euler, Problem 189: Tri-colouring a triangular grid

Edited by Jon E. Schoenfield, Jul 08 2017

Name simplified by Charles R Greathouse IV, Jul 09 2017

A169732 a(1) = 1000; for n>1, a(n) = a(n-1) - digitsum(a(n-1)).

Original entry on oeis.org

1000, 999, 972, 954, 936, 918, 900, 891, 873, 855, 837, 819, 801, 792, 774, 756, 738, 720, 711, 702, 693, 675, 657, 639, 621, 612, 603, 594, 576, 558, 540, 531, 522, 513, 504, 495, 477, 459, 441, 432, 423, 414, 405, 396, 378, 360, 351, 342, 333, 324, 315, 306, 297, 279, 261, 252, 243, 234, 225, 216, 207, 198, 180, 171, 162, 153, 144, 135, 126, 117, 108, 99, 81, 72, 63, 54, 45, 36, 27, 18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

N. J. A. Sloane, May 01 2010, based on a suggestion from Chris Cole

Cf. A169733, A000045, A004207, A007618, A065075, A010077, A065076, A065124, A169734, A169735.

f:=proc(n) global S; option remember; if n=1 then RETURN(S) else RETURN(f(n-1)-digsum(f(n-1))); fi; end; S:=1000; [seq(f(n),n=1..120)];

NestList[#-Total[IntegerDigits[#]]&,1000,100] (* Harvey P. Dale, Mar 28 2020 *)

A034927 Number of letters in "What is the next number in this sequence?".

Original entry on oeis.org

4, 2, 3, 4, 6, 2, 4, 8

Offset: 1

Chris Cole (chris(AT)questrel.com)

Compare "How I wish I could calculate Pi better today." - Harvey P. Dale, Sep 06 2022

Peter Foster (pfoster.No.SpaM(AT)pcug.org.au) in rec.puzzles.

Offset corrected by Arkadiusz Wesolowski, Jul 26 2011

A028505 Number of primes <= 100*n.

Original entry on oeis.org

25, 46, 62, 78, 95, 109, 125, 139, 154, 168, 184, 196, 211, 222, 239, 251, 266, 278, 290, 303, 317, 327, 342, 357, 367, 378, 393, 407, 419, 430, 442, 452, 463, 478, 489, 503, 516, 528, 539, 550, 565, 574, 590, 599, 610, 622, 634, 646, 654, 669, 681, 692, 702

Offset: 1

Chris Cole (chris(AT)questrel.com)

nonn

Fred W. Helenius (fredh(AT)ix.netcom.com), posting to newsgroup rec.puzzles, Dec. 1997.

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
J. Betrema, Table et repartition des nombres premiers inferieurs a 10000
A. Booker, The Nth Prime Page
Thomas Ehrenborg, Gauss Circle Primes, arXiv:2502.06804 [math.GM], 2025. See Table 2 p. 4.
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A000720, A038801, A038812, A038813, A038814, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

for n:1 through 50 do print(prime_pi(100*n));

Table[ PrimePi[ n*100 ], {n, 55}] (* Robert G. Wilson v, Jan 29 2003 *)

a(n)=primepi(100*n) \\ Charles R Greathouse IV, Apr 28 2015

A019271 A self-descriptive sequence: positions of consonants in "zero, two, four, ...".

Original entry on oeis.org

0, 2, 4, 5, 7, 10, 11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 29, 30, 32, 33, 36, 37, 39, 40, 43, 44, 46, 48, 49, 52, 53, 55, 57, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 85, 86, 87, 89, 90, 91, 92, 94, 95, 96, 98, 99, 100, 103, 104, 105, 106, 107

Offset: 0

chris(AT)questrel.questrel.com (Chris Cole)

Sean A. Irvine, Java program (github)

a(38) onwards corrected by Sean A. Irvine, Mar 04 2019

cp's OEIS Frontend

User: Chris Cole

A166736 Consider triangles stacked so the k-th row has 2*k-1 triangles. a(n) is the number of ways to color each triangle in the first n rows using three colors with the restriction that adjacent triangles must be different colors. (Triangles are adjacent if they share a side.)

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A169732 a(1) = 1000; for n>1, a(n) = a(n-1) - digitsum(a(n-1)).

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Maple

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A034927 Number of letters in "What is the next number in this sequence?".

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A028505 Number of primes <= 100*n.

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Macsyma

Mathematica

PARI

A019271 A self-descriptive sequence: positions of consonants in "zero, two, four, ...".

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