A378135 -id:A378135 - cp's OEIS frontend

A378136 a(n) = p(2np(n)), where p(x) = least prime > x.

2, 5, 13, 31, 41, 71, 89, 157, 179, 199, 223, 293, 313, 443, 479, 521, 547, 647, 691, 877, 929, 967, 1013, 1361, 1399, 1451, 1511, 1567, 1627, 1801, 1861, 2297, 2371, 2447, 2521, 2591, 2671, 3037, 3119, 3203, 3299, 3527, 3613, 4049, 4139, 4231, 4327, 4987, 5099

Offset: 0

Clark Kimberling, Nov 20 2024

nonn

			p(0) = 2, so a(0) = p(2*p(0)) = 5.

Cf. A000040, A013636, A151800, A378135.

Table[NextPrime[2 n*NextPrime[n]], {n, 0, 80}]

p(n) = nextprime(n+1);
a(n) = p(2*n*p(n)); \\ Michel Marcus, Nov 21 2024

A378137 a(n) = p(n^2*p(n)), where p(x) is the least prime > x.

Original entry on oeis.org

2, 3, 13, 47, 83, 179, 257, 541, 709, 907, 1103, 1579, 1873, 2879, 3343, 3833, 4357, 5501, 6163, 8311, 9203, 10151, 11149, 15349, 16729, 18127, 19609, 21143, 22739, 26083, 27901, 35569, 37889, 40343, 42773, 45329, 47963, 56131, 59207, 62383, 65609, 72287

Offset: 0

Clark Kimberling, Dec 21 2024

nonn

			p(2) = 3, so a(2) = p(4*p(2)) = 13.

Cf. A000040, A151800, A378135, A378136.

Table[NextPrime[n^2*NextPrime[n]], {n, 0, 80}]

a(n) = A151800(n^2*A151800(n)).

A379405 a(n) = p((n+1)*p(n)), where p(x) = least prime > x; i.e., p = A151800.

Original entry on oeis.org

3, 5, 11, 23, 29, 43, 53, 89, 101, 113, 127, 157, 173, 239, 257, 277, 293, 347, 367, 461, 487, 509, 541, 701, 727, 757, 787, 821, 853, 937, 967, 1187, 1223, 1259, 1297, 1361, 1373, 1559, 1601, 1657, 1693, 1811, 1861, 2069, 2129, 2179, 2213, 2549, 2609, 2657

Offset: 0

Clark Kimberling, Jan 18 2025

nonn

			p(1) = 2, so a(1) = p(2*p(1)) = 5.

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Cf. A000040, A053024, A151800, A378135, A378136, A378137.

Table[NextPrime[(n+1)*NextPrime[n]], {n, 0, 80}]

p(n) = nextprime(n+1);
a(n) = p((n+1)*p(n)); \\ Michel Marcus, Jan 18 2025

from sympy import nextprime
def A379405(n): return nextprime((n+1)*nextprime(n)) # Chai Wah Wu, Jan 20 2025

a(n) = A151800(A053024(n+1)). - Alois P. Heinz, Jan 18 2025

A380329 a(n) = A151800((n-1)*A151800(n)).

Original entry on oeis.org

2, 2, 5, 11, 17, 29, 37, 67, 79, 89, 101, 131, 149, 211, 223, 239, 257, 307, 331, 419, 439, 461, 487, 641, 673, 701, 727, 757, 787, 877, 907, 1117, 1151, 1187, 1223, 1259, 1297, 1481, 1523, 1559, 1601, 1721, 1777, 1979, 2027, 2069, 2129, 2441, 2503, 2549, 2609

Offset: 0

Clark Kimberling, Jan 21 2025

nonn

			p(1) = 2, so a(1) = p(0*p(1)) = 2.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A000040, A151800, A378135, A379405.

seq(nextprime((n-1)*nextprime(n)), n=0..100); # Robert Israel, Jan 23 2025

Table[NextPrime[(n-1)*NextPrime[n]], {n, 0, 80}]

p(n) = nextprime(n+1);
a(n) = p((n-1)*p(n)); \\ Michel Marcus, Jan 23 2025

cp's OEIS Frontend

A378136 a(n) = p(2*n*p(n)), where p(x) = least prime > x.

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A378137 a(n) = p(n^2*p(n)), where p(x) is the least prime > x.

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A379405 a(n) = p((n+1)*p(n)), where p(x) = least prime > x; i.e., p = A151800.

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A380329 a(n) = A151800((n-1)*A151800(n)).

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A378136 a(n) = p(2np(n)), where p(x) = least prime > x.