A061067 -id:A061067 - cp's OEIS frontend

A081717 Primes prime(j) such that prime(j) + j is composite.

5, 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 67, 71, 73, 83, 97, 103, 107, 109, 113, 127, 137, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 331, 337, 347

Offset: 1

Labos Elemer, Apr 02 2003

nonn

			127 is the 31st prime and 127+31 = 158 is composite.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A061067, A061068.

Do[s=Prime[n]+n; If[ !PrimeQ[s], Print[Prime[n]]], {n, 1, 100}]

A253971 Prime(n) is included iff prime(n) + n^2 is also prime.

Original entry on oeis.org

2, 3, 7, 19, 37, 43, 79, 113, 151, 163, 193, 229, 251, 281, 317, 373, 397, 433, 463, 503, 577, 757, 827, 911, 953, 997, 1069, 1123, 1321, 1399, 1423, 1481, 1657, 1693, 1747, 2029, 2143, 2267, 2311, 2473, 2503, 2551, 2593, 2687, 2753, 2791, 2917, 3313, 3323

Offset: 1

Vincenzo Librandi, Feb 04 2015

nonn

			7 is in this sequence because 7+16=23.
19 is in this sequence because 19+64=83.

Cf. A064711, A061067.

[NthPrime(n): n in [1..500] | IsPrime(NthPrime(n)+n^2)];

Prime[Select[Range[500], PrimeQ[Prime[#] + #^2] &]]

lista(nn) = forprime (n=2, nn, if (isprime(n+primepi(n)^2), print1(n, ", "))); \\ Michel Marcus, Feb 04 2015

a(n) = prime(A064711(n)). - Michel Marcus, Feb 04 2015

A254867 Numbers n such that prime(n) + n and prime(n) + n^2 are prime.

Original entry on oeis.org

1, 2, 4, 22, 66, 96, 106, 144, 180, 222, 324, 378, 466, 492, 604, 742, 760, 778, 784, 960, 984, 990, 994, 1050, 1150, 1162, 1186, 1248, 1302, 1308, 1356, 1360, 1380, 1744, 1830, 1866, 1870, 1956, 2052, 2070, 2112, 2182, 2212, 2380, 2470, 2556, 2586, 2638, 2676, 2760, 2766

Offset: 1

Zak Seidov, Feb 09 2015

nonn

			a(4) = 22 = A064402(6): prime(22) = 79, 79 + {22, 22^2} = {101, 563} both prime.

Subsequence of A064402. Cf. A000040, A014688, A061067, A061068.

A254867:=n->`if`(isprime(ithprime(n)+n) and isprime(ithprime(n)+n^2), n, NULL): seq(A254867(n), n=1..10^4); # Wesley Ivan Hurt, Jan 16 2017

Select[Range[1000], PrimeQ[Prime[#] + #] && PrimeQ[Prime[#] + #^2] &] (* Alonso del Arte, Feb 09 2015 *)
Select[Range[3000],AllTrue[Prime[#]+{#,#^2},PrimeQ]&] (* Harvey P. Dale, Jan 17 2023 *)

A084294 Number of primes in the interval [prime(n),n+prime(n)].

Original entry on oeis.org

2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 5, 5, 5, 5, 4, 5, 5, 7, 6, 6, 5, 5, 5, 5, 7, 7, 7, 7, 8, 7, 8, 9, 8, 8, 7, 7, 9, 8, 9, 8, 9, 11, 10, 10, 11, 10, 10, 9, 10, 11, 10, 9, 9, 9, 8, 10, 11, 11, 10, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 14, 15, 14, 13

Offset: 1

Labos Elemer, May 27 2003

nonn

Cf. A000040, A000720, A061067, A061068, A084295.

t[x_] := Table[w, {w, Prime[x], x+Prime[x]}] Table[Count[PrimeQ[t[n]], True], {n, 1, 128}] (* or *) Table[PrimePi[n+Prime[n]]-n+1, {n, 1, 25}];

a(n) = primepi(n+prime(n)) - n + 1; \\ Michel Marcus, Aug 28 2019

a(n) = Pi(n+prime(n)) - n + 1 = A000720(n+A000040(n)) - n + 1. [corrected by Michel Marcus, Aug 28 2019]

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A081717 Primes prime(j) such that prime(j) + j is composite.

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A253971 Prime(n) is included iff prime(n) + n^2 is also prime.

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A254867 Numbers n such that prime(n) + n and prime(n) + n^2 are prime.

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A084294 Number of primes in the interval [prime(n),n+prime(n)].

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