A158611 -id:A158611 - cp's OEIS frontend

A163248 Sum of the n-th composite number plus the number of composite numbers less than the n-th noncomposite number.

4, 6, 8, 10, 12, 17, 20, 24, 26, 31, 38, 40, 46, 51, 53, 57, 63, 69, 72, 79, 83, 85, 91, 95, 102, 110, 114, 117, 122, 124, 128, 143, 147, 153, 155, 165, 168, 174, 180, 184, 190, 197, 200, 210, 212, 216, 218, 231, 243, 247

Offset: 1

Jaroslav Krizek, Jul 23 2009

Bo Gyu Jeong, Table of n, a(n) for n = 1..10000

nnc:= 1: nc:= 0; b[nnc]:= 0:b[0]:= 0:
for x from 2 to 1000 do
   if isprime(x) then
     nnc:= nnc+1; b[nnc]:= b[nnc-1];
   else
     b[nnc]:= b[nnc]+1;
     nc:= nc+1;
     c[nc]:= x;
   fi
od:
seq(b[n-1]+c[n],n=1..min(nnc,nc)); # Robert Israel, Jan 09 2015

a(n) = A002808(n) + A162177(n) = A008578(n) + A073169(n).

Corrected for Aug 2009 change of offset in A158611 and A008578 by Jaroslav Krizek, Jan 27 2010

A167136 a(n) = b(n)-th highest positive integer not equal to any a(k), 1 <= k <= n-1, where b(n) = noncomposite numbers = A008578(n).

Original entry on oeis.org

1, 3, 5, 8, 11, 16, 19, 24, 27, 32, 39, 42, 49, 54, 57, 62, 69, 76, 79, 86, 91, 94, 101, 106, 113, 122, 127, 130, 135, 138, 143, 158, 163, 170, 173, 184, 187, 194, 201, 206, 213, 220, 223, 234, 237, 242, 245, 258, 271, 276, 279, 284, 291, 294, 305, 312, 319, 326

Offset: 1

Jaroslav Krizek, Oct 28 2009

nonn

a(1) = 1, a(n) = A014688(n-1) = (n-1)-th prime + n - 1 for n >= 2. a(n) = A090178(n) - 1 = n-th noncomposite number + n - 1 for n >= 2.

			A008578(4) = 5, so a(4) = 8 = 5th highest positive integer not equal to 1, 3, or 5 (the values of a(k), 1 <= k <= 3).

a(1) = 1, a(n) = a(n-1) + A008578(n+1) - A008578(n) + 1 for n >= 2. a(1) = 1, a(2) = 3, a(n) = a(n-1) + A001223(n) + 1 for n >= 3. a(1) = 1, a(n) = n - 1 + A000040(n-1) = n - 1 + A008578(n) = n - 1 + A158611(n+1) for n >= 2.

A182155 Integers of the form: 0/3 + 1/3 + 2/3 + 3/3 + 5/3 + 7/3 + 11/3 + 13/3 + 17/3 + ....

Original entry on oeis.org

0, 1, 2, 6, 14, 26, 66, 94, 147, 264, 663, 759, 916, 1089, 1213, 1343, 1554, 1706, 2113, 2473, 2661, 2861, 3069, 3285, 3513, 3747, 3989, 4497, 4763, 5039, 5323, 5911, 6217, 6527, 6849, 7179, 7690, 8227, 8790, 9566, 9966, 10995, 11423, 12076, 12974, 13438

Offset: 1

Gerasimov Sergey, Apr 15 2012

nonn

Numbers k such that the sum of first n nonnegative noncomposite numbers is equal to 3k.

			1/3 + 2/3 = 1, 1/3 + 2/3 + 3/3 = 2, 1/3 + 2/3 + 3/3 + 5/3 + 7/3 = 6.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A007504, A154293, A158611.

s = 1; t = {0}; Do[s = s + Prime[n]; If[Mod[s, 3] == 0, AppendTo[t, s/3]], {n, 200}]; t (* T. D. Noe, Apr 18 2012 *)
Select[Accumulate[Join[{0,1/3},Prime[Range[200]]/3]],IntegerQ] (* Harvey P. Dale, Mar 06 2016 *)

Definition corrected by Harvey P. Dale, Mar 06 2016

A159900 Concatenation of the first n elements of A008578.

Original entry on oeis.org

1, 12, 123, 1235, 12357, 1235711, 123571113, 12357111317, 1235711131719, 123571113171923, 12357111317192329, 1235711131719232931, 123571113171923293137, 12357111317192329313741

Offset: 1

Jaroslav Krizek, Apr 25 2009

Cf. A158611.

Prepend 1 to the terms of A019518(n) - R. J. Mathar, Apr 28 2009.

Slightly edited by R. J. Mathar, Apr 28 2009

Correction for change of offset in A158611 and A008578 in Aug 2009 Jaroslav Krizek, Jan 27 2010

A162988 n appears A008578(n) times.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset: 1

Jaroslav Krizek, Jul 19 2009

nonn

a(n) ~ 2 sqrt(n / log n)

Formula and more terms from Charles R Greathouse IV, Nov 02 2009

Correction for change of offset in A158611 and A008578 in Aug 2009 Jaroslav Krizek, Jan 27 2010

A173137 n-th nonnegative noncomposite number plus n.

Original entry on oeis.org

1, 3, 5, 7, 10, 13, 18, 21, 26, 29, 34, 41, 44, 51, 56, 59, 64, 71, 78, 81, 88, 93, 96, 103, 108, 115, 124, 129, 132, 137, 140, 145, 160, 165, 172, 175, 186, 189, 196, 203, 208, 215, 222, 225, 236, 239, 244, 247, 260, 273, 278, 281, 286, 293, 296, 307, 314, 321

Offset: 1

Juri-Stepan Gerasimov, Feb 10 2010

			a(1) = 0 + 1 = 1, a(2) = 1 + 2 = 3, a(3) = 2 + 3 = 5,
a(4) = 3 + 4 = 7, a(5) = 5 + 5 = 10.

[1] cat [NthPrime(n-1)+n+1: n in [1..58] ]; // Vincenzo Librandi, Dec 08 2015

Join[{1}, Table[Prime[n - 1] + n + 1, {n, 2, 60}]] (* Vincenzo Librandi, Dec 08 2015 *)

a(n) = A158611(n) + A000027(n).

Corrected by Charles R Greathouse IV, Mar 25 2010

A176098 a(n) = prime(n) times the n-th nonnegative noncomposite.

Original entry on oeis.org

0, 3, 10, 21, 55, 91, 187, 247, 391, 551, 713, 1073, 1271, 1591, 1927, 2279, 2773, 3233, 3953, 4331, 4891, 5609, 6059, 7031, 8051, 8989, 9991, 10807, 11227, 12091, 13843, 14803, 17399, 18209, 20413, 20989, 23393, 24613, 26219, 28199, 29893, 31313

Offset: 1

Juri-Stepan Gerasimov, Apr 08 2010

			a(5) = prime(5)*(nonnegative noncomposite(5)) = 11*5 = 55.

Cf. A000040, A158611.

Essentially the same as A090076.

a(n) = A000040(n)*A158611(n).

Entries checked by R. J. Mathar, Apr 16 2010

A226843 a(n) = prime(prime(n + 1) - 2).

Original entry on oeis.org

2, 5, 11, 23, 31, 47, 59, 73, 103, 109, 149, 167, 179, 197, 233, 269, 277, 313, 347, 353, 389, 419, 449, 499, 523, 547, 571, 587, 607, 691, 727, 761, 773, 853, 859, 907, 947, 977, 1019, 1051, 1063, 1129, 1153, 1187, 1201, 1289, 1381, 1427, 1433, 1453, 1489

Offset: 1

Juri-Stepan Gerasimov, Jun 19 2013

nonn

			a(5) = 31 since the (5 + 1)-th prime is 13, and the (13 - 2)-th prime is 31.

Cf. A158611, A006450.

Table[Prime[Prime[n] - 2], {n, 2, 75}] (* Alonso del Arte, Jun 21 2013 *)

a(n) = prime(prime(n + 1) - 2); \\ Michel Marcus, Nov 13 2016

cp's OEIS Frontend

A163248 Sum of the n-th composite number plus the number of composite numbers less than the n-th noncomposite number.

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A167136 a(n) = b(n)-th highest positive integer not equal to any a(k), 1 <= k <= n-1, where b(n) = noncomposite numbers = A008578(n).

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A182155 Integers of the form: 0/3 + 1/3 + 2/3 + 3/3 + 5/3 + 7/3 + 11/3 + 13/3 + 17/3 + ....

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A159900 Concatenation of the first n elements of A008578.

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A162988 n appears A008578(n) times.

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A173137 n-th nonnegative noncomposite number plus n.

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A176098 a(n) = prime(n) times the n-th nonnegative noncomposite.

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A226843 a(n) = prime(prime(n + 1) - 2).

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