A067563 -id:A067563 - cp's OEIS frontend

A038529 n-th prime - n-th composite.

-2, -3, -3, -2, 1, 1, 3, 4, 7, 11, 11, 16, 19, 19, 22, 27, 32, 33, 37, 39, 40, 45, 48, 53, 59, 62, 63, 65, 65, 68, 81, 83, 88, 89, 98, 99, 103, 108, 111, 116, 121, 121, 129, 130, 133, 134, 145, 155, 158, 159, 161, 165, 166, 175, 180, 185, 189, 190, 195, 197, 198, 207

Offset: 1

Vasiliy Danilov (danilovv(AT)usa.net), Jul 14 1998

Sequence is monotonically increasing starting from a(2). a(n) = a(n+1) if and only if both prime(n)+2 and composite(n)+1 are prime. - Jianing Song, Jun 27 2021

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A014237, A067563.

a038529 n = a000040 n - a002808 n  -- Reinhard Zumkeller, Apr 30 2014

composite[n_Integer] := Block[{k=n+PrimePi[n]+1}, While[k-PrimePi[k]-1 != n, k++]; k]; Table[Prime[n] - composite[n], {n,65}] (* corrected by Harvey P. Dale, Aug 08 2011 *)
Module[{nn=300,prs,cmps,len},prs=Prime[Range[PrimePi[nn]]];cmps= Complement[ Range[4,nn],prs];len=Min[Length[prs],Length[cmps]]; #[[1]]- #[[2]]&/@ Thread[{Take[prs,len],Take[cmps,len]}]] (* Harvey P. Dale, Jun 18 2015 *)

from sympy import prime, composite
def A038529(n):
    return prime(n)-composite(n) # Chai Wah Wu, Dec 27 2018

a(n) = A000040(n) - A002808(n). - Reinhard Zumkeller, Apr 30 2014

A133019 Product of n-th prime and n-th prime written backwards.

Original entry on oeis.org

4, 9, 25, 49, 121, 403, 1207, 1729, 736, 2668, 403, 2701, 574, 1462, 3478, 1855, 5605, 976, 5092, 1207, 2701, 7663, 3154, 8722, 7663, 10201, 31003, 75007, 98209, 35143, 91567, 17161, 100147, 129409, 140209, 22801, 117907, 58843, 127087

Offset: 1

Omar E. Pol, Oct 27 2007

a(8) = 1729 is the second taxicab number, also called the Hardy-Ramanujan number (see A001235, A011541 and A133029).

			a(8) = 1729 because the 8th prime is 19 and 19 written backwards is 91 and 19*91 = 1729.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A001235, A004087, A011541, A061205, A067563, A067087, A133029. Prime numbers: A000040.

#*FromDigits[Reverse[IntegerDigits[#]]] & /@ Prime[Range[1, 50]] (* G. C. Greubel, Oct 02 2017 *)
#*IntegerReverse[#]&/@Prime[Range[40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 29 2021 *)

vector(60, n, prime(n)*subst(Polrev(digits(prime(n))), x, 10)) \\ Michel Marcus, Dec 17 2014

a(n) = A000040(n) * A004087(n)

A127118 a(n) = n-th prime * n-th nonprime.

Original entry on oeis.org

2, 12, 30, 56, 99, 130, 204, 266, 345, 464, 558, 740, 861, 946, 1128, 1325, 1534, 1647, 1876, 2130, 2336, 2607, 2822, 3115, 3492, 3838, 4017, 4280, 4578, 4972, 5715, 6026, 6576, 6811, 7450, 7701, 8164, 8802, 9185, 9688, 10203, 10498, 11460, 11966, 12411

Offset: 1

Neven Juric (neven.juric(AT)apis-it.hr), Mar 21 2007

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

Cf. A000040, A018252, A002808.

Cf. A014237, A064799, A067563.

a127118 n = a000040 n * a018252 n  -- Reinhard Zumkeller, Apr 30 2014

Module[{nn=100,prs,non,len},prs=Prime[Range[nn]];non=Complement[ Range[ nn],prs]; len=Min[Length[prs],Length[non]]; Times@@#&/@ Thread[ {Take[ prs,len],Take[non,len]}]] (* Harvey P. Dale, Dec 29 2012 *)

from sympy import prime, composite
def A127118(n):
    return 2 if n == 1 else prime(n)*composite(n-1) # Chai Wah Wu, Dec 27 2018

a(n) = A000040(n) * A018252(n).

A331999 a(n) is the product of n, the n-th prime and the n-th composite number.

Original entry on oeis.org

8, 36, 120, 252, 550, 936, 1666, 2280, 3312, 5220, 6820, 9324, 11726, 14448, 17625, 22048, 27081, 30744, 38190, 45440, 50589, 59092, 66815, 76896, 92150, 102414, 111240

Offset: 1

Soham B. Patel, Feb 04 2020

nonn

			For n=1; prime(1)=2, composite(1)=4; a(1) = 8;
For n=2; prime(2)=3, composite(2)=6; a(2) = 36;
For n=3; prime(3)=5, composite(3)=8; a(3) = 120.

Cf. A000040, A002808, A067563.

m = 105; p = Select[Range[m], PrimeQ]; n = Length[p]; c = Complement[Range[2, m], p][[1;;n]]; p * c * Range[n] (* Amiram Eldar, Feb 12 2020 *)

a(n) = n*prime(n)*composite(n).

a(n) = n*A067563(n).

cp's OEIS Frontend

A038529 n-th prime - n-th composite.

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A133019 Product of n-th prime and n-th prime written backwards.

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A127118 a(n) = n-th prime * n-th nonprime.

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A331999 a(n) is the product of n, the n-th prime and the n-th composite number.

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