A065042 -id:A065042 - cp's OEIS frontend

A100486 a(n) = pi(n) + prime(n).

2, 4, 7, 9, 14, 16, 21, 23, 27, 33, 36, 42, 47, 49, 53, 59, 66, 68, 75, 79, 81, 87, 92, 98, 106, 110, 112, 116, 119, 123, 138, 142, 148, 150, 160, 162, 169, 175, 179, 185, 192, 194, 205, 207, 211, 213, 226, 238, 242, 244, 248, 254, 257, 267, 273, 279, 285, 287

Offset: 1

Jonathan Vos Post, Nov 22 2004

			a(21) = pi(21) + prime(21) = 8 + 73 = 81.

Indranil Ghosh, Table of n, a(n) for n = 1..10410

Cf. A000040, A000720, A065042, A100917.

[#PrimesUpTo(n) + NthPrime(n): n in [1..80]]; // G. C. Greubel, Apr 04 2023

with(numtheory); A100486:=n->pi(n) + ithprime(n); seq(A100486(n), n=1..60); # Wesley Ivan Hurt, Jan 28 2014

Mathematica
```
Table[PrimePi[n] + Prime[n], {n, 60}]
```

a(n) = primepi(n) + prime(n); \\ Michel Marcus, Feb 24 2023

[prime_pi(n) + nth_prime(n) for n in range(1,81)] # G. C. Greubel, Apr 04 2023

a(n) = A000720(n) + A000040(n). - Wesley Ivan Hurt, Jan 28 2014

A100917 Primes of the form pi(n) + prime(n).

Original entry on oeis.org

2, 7, 23, 47, 53, 59, 79, 179, 211, 257, 311, 331, 373, 379, 431, 443, 487, 491, 503, 523, 647, 661, 673, 677, 683, 691, 857, 863, 887, 919, 947, 1009, 1021, 1091, 1129, 1151, 1171, 1193, 1231, 1237, 1277, 1283, 1471, 1663, 1667, 1753, 1777, 1811, 1993

Offset: 1

Ray Chandler, Nov 27 2004

nonn

Primes appearing in A100486.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A065042, A100486.

Select[Table[PrimePi[n] + Prime[n], {n, 300}], PrimeQ]

a(n) = A100486(A065042(n)).

A065046 Numbers k such that prime(k) - pi(k) is a prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 9, 14, 15, 16, 19, 22, 30, 38, 44, 55, 64, 79, 81, 90, 91, 93, 94, 96, 101, 113, 115, 117, 118, 121, 122, 123, 124, 125, 133, 142, 148, 163, 173, 176, 178, 182, 183, 185, 189, 190, 199, 205, 206, 208, 223, 226, 232, 239, 240, 251, 253, 255, 263

Offset: 1

Robert G. Wilson v, Nov 05 2001

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A065042, A111181.

Select[Range[300], PrimeQ[Prime[ # ] - PrimePi[ # ]] & ]

isok(m) = isprime(prime(m) - primepi(m)); \\ Harry J. Smith, Oct 04 2009

A065059 Primes p such that prime(p) + pi(p) is a prime.

Original entry on oeis.org

3, 13, 53, 71, 113, 181, 397, 463, 479, 557, 593, 647, 683, 701, 719, 743, 769, 863, 941, 983, 1069, 1091, 1109, 1181, 1193, 1231, 1277, 1291, 1307, 1451, 1733, 1811, 1931, 2347, 2393, 2411, 2473, 2531, 2551, 2593, 2887, 3041, 3221, 3251, 3347, 3361

Offset: 1

Robert G. Wilson v, Nov 06 2001

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A065042.

Select[Prime[Range[500]],PrimeQ[Prime[#]+PrimePi[#]]&] (* Harvey P. Dale, Oct 12 2014 *)

{ n=0; default(primelimit, 4294965247); for (m=1, 10^9, p=prime(m); if (isprime(prime(p) + primepi(p)), write("b065059.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 05 2009

A224872 Numbers k such that prime(k)*pi(k)+1 is prime.

Original entry on oeis.org

3, 15, 20, 29, 58, 63, 80, 90, 92, 93, 96, 116, 125, 126, 143, 151, 155, 156, 164, 182, 185, 189, 210, 230, 251, 255, 256, 268, 274, 275, 294, 298, 319, 323, 324, 325, 328, 330, 343, 360, 362, 399, 400, 416, 425, 429, 437, 446, 457, 463, 466, 480, 497, 505, 506

Offset: 1

K. D. Bajpai, Jul 23 2013

nonn

			Prime(126)*pi(126)+1 = 701*30+1 = 21031 which is prime, hence 126 is in the sequence.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A065042.

A224872:=proc(n) local a; a:=(ithprime(n)*numtheory[pi](n)+1) ; if isprime(a) then RETURN(n) end if:end proc: seq(A224872(n),n=1..600);

Select[Range[2000],PrimeQ[Prime[#]*PrimePi[#]+1]&]

n=0;forprime(p=2,1e5,if(isprime(p*primepi(n++)+1), print1(n", "))) \\ Charles R Greathouse IV, Jul 23 2013

cp's OEIS Frontend

A100486 a(n) = pi(n) + prime(n).

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A100917 Primes of the form pi(n) + prime(n).

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A065046 Numbers k such that prime(k) - pi(k) is a prime.

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A065059 Primes p such that prime(p) + pi(p) is a prime.

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A224872 Numbers k such that prime(k)*pi(k)+1 is prime.

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Maple

Mathematica

PARI