A179545 -id:A179545 - cp's OEIS frontend

A179802 Digital root of A179545.

3, 9, 3, 9, 3, 9, 3, 9, 3, 3, 9, 9, 3, 9, 3, 3, 3, 9, 9, 3, 9, 9, 3, 3, 9, 3, 9, 3, 9, 3, 9, 3, 3, 9, 3, 9, 9, 9, 3, 3, 3, 9, 3, 9, 3, 9, 9, 9, 3, 9, 3, 3, 9, 3, 3, 3, 3, 9, 9, 3, 9, 3, 9, 3, 9, 3, 9, 9, 3, 9, 3, 3, 9, 9, 9, 3, 3, 9, 3, 9, 3, 9, 3, 9, 9, 3, 3

Offset: 1

Odimar Fabeny, Jul 27 2010

Because every term in A179545 is a multiple of 3, each term of this sequence is 3 or 9. - Nathaniel Johnston, May 04 2011

a(n) = 3 if and only if prime(n) == 2 (mod 3); otherwise a(n) = 9. - Charles R Greathouse IV, May 19 2011

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A000040, A010888, A179545.

read("transforms") ; A010888 :=proc(n) local a; a := digsum(n) ; if a > 9 then return procname(a) ; else return a; end if; end proc:
A179545 := proc(n) local p; p := ithprime(n); 3*p*(p-1)/2 ; end proc:
A179802 := proc(n) A010888(A179545(n)) ; end proc:
seq(A179802(n),n=1..180) ; # R. J. Mathar, Oct 03 2010

apply(p->if(p%3==2,3,9),primes(10000)) \\ Charles R Greathouse IV, May 19 2011

a(n) = A010888(A179545(n)). - Michel Marcus, Mar 08 2022

More terms from R. J. Mathar, Oct 03 2010

A001748 a(n) = 3 * prime(n).

Original entry on oeis.org

6, 9, 15, 21, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381, 393, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 699, 717, 723, 753

Offset: 1

N. J. A. Sloane

Semiprimes divisible by 3. - Jianing Song, Oct 02 2022

Paolo P. Lava, Table of n, a(n) for n = 1..20000
Eric Weisstein's World of Mathematics, Skeleton

Subsequence of A001358.

Cf. A000040, A100484, A253046, A164023, A164024, A179545, A253046.

a001748 = (* 3) . a000040  -- Reinhard Zumkeller, Dec 26 2014

[3*p: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 26 2014

Prime[Range[22]]*3 (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

3*primes(22) \\ Charles R Greathouse IV, May 19 2011

A164023(a(n)) = A164024(a(n)) = A000040(n). - Reinhard Zumkeller, Aug 09 2009
a(n) = 3*A000040(n). - Omar E. Pol, Jan 31 2012
A253046(a(n)) < a(n). - Reinhard Zumkeller, Dec 26 2014

A179896 Sum of the numbers between k := n-th nonprime and 2k (like a jump in a Sieve of Eratosthenes).

Original entry on oeis.org

0, 18, 45, 84, 108, 135, 198, 273, 315, 360, 459, 570, 630, 693, 828, 900, 975, 1053, 1134, 1305, 1488, 1584, 1683, 1785, 1890, 2109, 2223, 2340, 2583, 2838, 2970, 3105, 3384, 3528, 3675, 3825, 3978, 4293, 4455, 4620, 4788, 4959, 5310, 5673, 5859, 6048, 6240, 6435

Offset: 1

Odimar Fabeny, Jul 31 2010

The values 4, 7, 10... (A016777 for n>1) are the values of floor( a(k)/ A018252(k) ) where k runs through the indices where A179879(k) mod A018252(k) != 0. - Odimar Fabeny.

Proof: a(k)/A018252(k) is 3*(A081252(k)-1)/2. This is a non-integer iff A018252(k) is even. Since the n-th even nonprime is 2*n+2, floor(3*(2*n+1)/2) = 3*n+1=a(n). - Robert Israel, Aug 27 2014

			0(0) = 0, 1(2) = 0, 4(8) = 5,6,7 = 18, 6(12) = 7,8,9,10,11 = 45 and so on.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A000040, A179545.

ithnonprime := proc(n)local k: option remember: if(n=1)then return 1: else k := procname(n-1)+1: while true do if(not isprime(k))then return k fi: k:=k+1: od: fi: end:
A179896 := proc(n)local k: k:=ithnonprime(n): return 3*k*(k-1)/2: end:
seq(A179896(n),n=1..40); # Nathaniel Johnston, Apr 21 2011

f[n_] := Plus @@ Range[n + 1, 2 n - 1]; f /@ Select[ Range@ 64, ! PrimeQ@# &] (* Robert G. Wilson v, Sep 02 2010 *)

a(n) = A045943(A141468(n+1)-1). - R. J. Mathar, Sep 01 2010

More terms from Odimar Fabeny, Aug 11 2010

Offset adapted to A141468 and to match another 0 - R. J. Mathar, Sep 01 2010

A273221 a(n) = p(p - 1)(13*p - 5)/6, where p = prime(n).

Original entry on oeis.org

7, 34, 200, 602, 2530, 4264, 9792, 13794, 24794, 50344, 61690, 105672, 144320, 166754, 218362, 314184, 434594, 480680, 638242, 760410, 826944, 1049594, 1218274, 1503744, 1949312, 2201800, 2335834, 2620002, 2770344, 3088064, 4389882, 4819490, 5515072

Offset: 1

Vincenzo Librandi, May 18 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000
F. V. Weinstein, Notes on Fibonacci partitions, arXiv:math/0307150 [math.NT], 2003-2015, page 22.

Cf. A006093, A008837, A179545.

[p*(p-1)*(13*p-5)/6: p in PrimesUpTo(200)];

Table[p = Prime[n]; p (p - 1) (13 p - 5) / 6, {n, 40}]
#(#-1) (13#-5)/6&/@Prime[Range[40]] (* Harvey P. Dale, Aug 04 2021 *)

require 'prime'
p Prime.each.take(n).map{|i| i * (i - 1) * (13 * i - 5) / 6} # Seiichi Manyama, May 25 2016

A273222 a(n) = p(p - 1)(73p^2 - 45p + 14)/24, where p = prime(n).

Original entry on oeis.org

18, 134, 1345, 5733, 38280, 76479, 230588, 363546, 792649, 2033451, 2664915, 5454873, 8260270, 10012464, 14337303, 23275109, 35855716, 41007555, 59825238, 75546485, 84478374, 116064351, 141557994, 187394306, 264812328, 311476425, 336995709, 392705408, 423017991

Offset: 1

Vincenzo Librandi, May 19 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000
F. V. Weinstein, Notes on Fibonacci partitions, arXiv:math/0307150 [math.NT], 2003-2015, page 22.

Cf. A006093, A008837, A179545, A273221.

[p*(p-1)*(73*p^2-45*p+14)/24: p in PrimesUpTo(200)];

Table[p = Prime[n]; p (p - 1) (73 p^2 - 45 p + 14) / 24, {n, 40}]
(#(#-1)(73#^2-45#+14))/24&/@Prime[Range[30]] (* Harvey P. Dale, Jan 17 2017 *)

A179893 a(n) = 3/2 * (prime(n)-1).

Original entry on oeis.org

3, 6, 9, 15, 18, 24, 27, 33, 42, 45, 54, 60, 63, 69, 78, 87, 90, 99, 105, 108, 117, 123, 132, 144, 150, 153, 159, 162, 168, 189, 195, 204, 207, 222, 225, 234, 243, 249, 258, 267, 270, 285, 288, 294, 297, 315, 333, 339, 342, 348, 357, 360, 375, 384, 393, 402, 405

Offset: 2

Odimar Fabeny, Jul 30 2010, Aug 02 2010

			For n=4, the fourth prime is 7, so a(4) = (3/2) * (7 - 1) = 9. Note that since the sequence starts at n=2, prime(n) is odd, so a(n) is an integer. - _Michael B. Porter_, Jul 19 2016

G. C. Greubel, Table of n, a(n) for n = 2..1000

Cf. A000040, A179545.

[3/2*(NthPrime(n)-1): n in [2..60]]; // Vincenzo Librandi, Jun 18 2016

Table[(3/2)*(Prime[n] - 1), {n,2,100}] (* G. C. Greubel, Jun 17 2016 *)

a(n)=prime(n)\2*3 \\ Charles R Greathouse IV, May 19 2011

A179545 / prime(n).

a(n) = 3*A005097(n-1). - R. J. Mathar, Aug 15 2010

More terms from R. J. Mathar, Aug 15 2010

A179899 Integers of the form A179896(n)/A141468(n+1).

Original entry on oeis.org

0, 12, 21, 30, 36, 39, 48, 51, 57, 66, 72, 75, 81, 84, 93, 96, 102, 111, 114, 120, 126, 129, 135, 138, 141, 147, 156, 165, 171, 174, 177, 180, 183, 186, 192, 198, 201, 210, 213, 216, 219, 228, 231, 237, 240, 246, 252, 255, 261, 264, 273, 276, 279, 282, 291

Offset: 1

Odimar Fabeny, Jul 31 2010

			0 = 0/1, 12 = 108/9, 21 = 315/15, 30 = 630/21, 36 = 900/25 and so on.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A000040, A179545, A179896.

ithnonprime := proc(n)local k: option remember: if(n=1)then return 1: else k := procname(n-1)+1: while true do if(not isprime(k))then return k fi: k:=k+1: od: fi: end: A179899ind := proc(n) option remember: local k: if(n=1)then return 1:fi: for k from procname(n-1)+1 do if(ithnonprime(k) mod 2 <> 0)then return k: fi: od: end: A179899 := proc(n) return 3*(ithnonprime(A179899ind(n))-1)/2: end: seq(A179899(n),n=1..55); # Nathaniel Johnston, May 05 2011

More terms from Odimar Fabeny, Aug 12 2010

Definition rephrased by R. J. Mathar, Sep 01 2010

A273223 a(n) = p(p - 1)(501p^3 - 414p^2 + 111*p - 54)/120, where p = prime(n).

Original entry on oeis.org

42, 504, 8796, 53298, 566412, 1341756, 5312160, 9373536, 24790458, 80346588, 112613886, 275440284, 462452448, 588037212, 920759046, 1686448764, 2893307844, 3421602972, 5484429720, 7340452434, 8440231968, 12551864598, 16086117120, 22838112000, 35181089856

Offset: 1

Vincenzo Librandi, May 19 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000
F. V. Weinstein, Notes on Fibonacci partitions, arXiv:math/0307150 [math.NT], 2003-2015, page 22.

Cf. A006093, A008837, A179545, A273221, A273222.

[p*(p-1)*(501*p^3-414*p^2+111*p-54)/120: p in PrimesUpTo(200)];

Table[p = Prime[n]; p (p - 1) (501 p^3 - 414 p^2 + 111 p - 54) / 120, {n, 40}]

A179789 Sum of the differences between the first prime and the next, inside in the first jump in a Sieve of Eratosthenes table.

Original entry on oeis.org

1, 2, 2, 10, 16, 20, 34, 44, 66, 78, 124, 182, 184, 206, 212, 300, 386, 360, 412, 494, 466, 608, 628, 700, 928, 1046, 1006, 1034, 996, 1034, 1440, 1474, 1728, 1816, 1976, 1922, 2226, 2212, 2264, 2260, 2604, 2722, 2968, 3094, 3158, 3292, 3714, 4148, 4218, 4370

Offset: 0

Odimar Fabeny, Jul 27 2010

nonn

2 - 3 = 1, 3 - 5 = 2, 5 - 7 = 2, 7 - 11 = 4 + 7 - 13 = 6 ==> 4 + 6 = 10, 11 - 13 = 2 + 11 - 17 = 6 + 11 - 19 = 8 ==> 2 + 6 + 8 = 16.

Cf. A000040, A179545.

A179789 := proc(n) a :=0 ; for q from ithprime(n)+1 to 2*ithprime(n) do if isprime(q) then a := a+q-ithprime(n) ; end if; end do: a ; end proc: seq(A179789(n),n=1..50) ; # R. J. Mathar, Sep 19 2010

Extended by R. J. Mathar, Sep 19 2010

A273224 a(n) = p(p - 1)(4051p^4 - 4130p^3 + 1445p^2 - 190p + 264)/720, where p = prime(n).

Original entry on oeis.org

104, 1911, 56974, 488810, 8247965, 23154950, 120309952, 237557475, 761914054, 3119071046, 4675225940, 13662251406, 25431242200, 33922355957, 58079673968, 120014329006, 229294119649, 280383632390, 493768590887, 700437412570, 828128942424, 1333041982376

Offset: 1

Vincenzo Librandi, May 19 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000
F. V. Weinstein, Notes on Fibonacci partitions, arXiv:math/0307150 [math.NT], 2003-2015, page 22.

Cf. A006093, A008837, A179545, A273221, A273222, A273223.

[p*(p-1)*(4051*p^4-4130*p^3+1445*p^2-190*p+264)/720: p in PrimesUpTo(200)];

Table[p = Prime[n]; p (p - 1) (4051 p^4 - 4130 p^3 + 1445 p^2 - 190 p + 264) / 720, {n, 40}]
#(#-1) (4051#^4-4130#^3+1445#^2-190#+264)/720&/@Prime[Range[30]] (* Harvey P. Dale, Aug 05 2018 *)

cp's OEIS Frontend

A179802 Digital root of A179545.

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A001748 a(n) = 3 * prime(n).

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A179896 Sum of the numbers between k := n-th nonprime and 2k (like a jump in a Sieve of Eratosthenes).

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A273221 a(n) = p*(p - 1)*(13*p - 5)/6, where p = prime(n).

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A273222 a(n) = p*(p - 1)*(73*p^2 - 45*p + 14)/24, where p = prime(n).

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A179893 a(n) = 3/2 * (prime(n)-1).

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A179899 Integers of the form A179896(n)/A141468(n+1).

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A273221 a(n) = p(p - 1)(13*p - 5)/6, where p = prime(n).

A273222 a(n) = p(p - 1)(73p^2 - 45p + 14)/24, where p = prime(n).

A273223 a(n) = p(p - 1)(501p^3 - 414p^2 + 111*p - 54)/120, where p = prime(n).

A273224 a(n) = p(p - 1)(4051p^4 - 4130p^3 + 1445p^2 - 190p + 264)/720, where p = prime(n).