A004232 -id:A004232 - cp's OEIS frontend

A184935 Primes of the form k^2 + prime(k).

3, 7, 23, 83, 181, 239, 563, 1013, 1447, 1607, 2129, 2729, 3167, 3881, 4673, 5849, 6481, 7489, 8563, 9719, 11813, 18713, 21563, 25247, 27197, 29221, 33469, 36467, 47977, 50683, 51599, 56237, 69257, 71389, 75731, 96893, 107119, 115163

Offset: 1

Jonathan Vos Post, Feb 02 2011

Primes in A004232. Sequence A064711 has the values of k.

			3167 is here because 54^2 + prime(54) = 54^2 + 251 = 3167, which is prime.

Carmine Suriano, Table of n, a(n) for n = 1..82

Cf. A000040, A000290, A004232, A064711.

[ a: k in [0..10000] | IsPrime(a) where a is k^2 + NthPrime(k) ]; // Vincenzo Librandi, Apr 14 2011

Select[Table[k^2 + Prime[k], {k, 1000}], PrimeQ] (* Harvey P. Dale, Feb 16 2011 *)

Better name from Zak Seidov, Apr 12 2011

A064711 Numbers n such that n^2 + prime(n) is a prime.

Original entry on oeis.org

1, 2, 4, 8, 12, 14, 22, 30, 36, 38, 44, 50, 54, 60, 66, 74, 78, 84, 90, 96, 106, 134, 144, 156, 162, 168, 180, 188, 216, 222, 224, 234, 260, 264, 272, 308, 324, 336, 344, 366, 368, 374, 378, 390, 402, 406, 422, 466, 468, 476, 492, 498, 502, 516, 604, 624, 636

Offset: 1

Robert G. Wilson v, Oct 13 2001

			2 is in the sequence because 2^2 + Prime(2) = 4 + 3 = 7 is a prime.

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

Cf. A004232, A184935.

[ n: n in [1..700] | IsPrime(n^2+NthPrime(n)) ]; // Klaus Brockhaus, Apr 12 2011

Select[ Range[ 1000 ], PrimeQ[ #^2 + Prime[ # ] ] & ]

{ n=0; for (m=1, 10^9, if (isprime(m^2 + prime(m)), write("b064711.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 23 2009

A188831 Primes of the form k^2 - prime(k).

Original entry on oeis.org

23, 71, 107, 263, 487, 677, 787, 1427, 1583, 2081, 3319, 5393, 8713, 10247, 11071, 12377, 18257, 20477, 24659, 26573, 29243, 29927, 33487, 34949, 37223, 37991, 41981, 51449, 60917, 64937, 66977, 71167, 83357, 85667, 99013, 100271, 109313, 110629, 118757

Offset: 1

Zak Seidov, Apr 11 2011

nonn

Or, primes in A073497. Corresponding values of k in A064712.
This is to A073497 and A064712 as A184935 is to A004232 and A064711.
The two primes prime(k) and k^2-prime(k) are a Goldbach partition of k^2. - T. D. Noe, Apr 14 2011

			23 is here because 6^2 - prime(6) = 36 - 13 = 23.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A004232, A064711, A064712, A073497, A184935.

[ a: k in [0..10000] | IsPrime(a) where a is k^2-NthPrime(k) ]; // Vincenzo Librandi, Apr 14 2011

Select[Table[k^2 - Prime[k], {k, 1000}], PrimeQ] (* T. D. Noe, Apr 14 2011 *)

a(n) = A073497(A064712(n)).

A356868 a(n) = n^2 * prime(n).

Original entry on oeis.org

2, 12, 45, 112, 275, 468, 833, 1216, 1863, 2900, 3751, 5328, 6929, 8428, 10575, 13568, 17051, 19764, 24187, 28400, 32193, 38236, 43907, 51264, 60625, 68276, 75087, 83888, 91669, 101700, 122047, 134144, 149193, 160684, 182525, 195696, 214933, 235372, 254007, 276800, 300899

Offset: 1

Alex Ratushnyak, Sep 01 2022

Cf. A000040, A000290, A004232, A033286, A196421.

a[n_] := n^2 * Prime[n]; Array[a, 40] (* Amiram Eldar, Sep 02 2022 *)

from sympy import prime
def a(n): return n**2 * prime(n)
print([a(n) for n in range(1, 41)]) # Michael S. Branicky, Sep 01 2022

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A184935 Primes of the form k^2 + prime(k).

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A064711 Numbers n such that n^2 + prime(n) is a prime.

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A188831 Primes of the form k^2 - prime(k).

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A356868 a(n) = n^2 * prime(n).

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