A378136 -id:A378136 - cp's OEIS frontend

A378135 a(n) = p(n*p(n)), where p(x) = least prime > x.

2, 3, 7, 17, 23, 37, 43, 79, 89, 101, 113, 149, 157, 223, 239, 257, 277, 331, 347, 439, 461, 487, 509, 673, 701, 727, 757, 787, 821, 907, 937, 1151, 1187, 1223, 1259, 1297, 1361, 1523, 1559, 1601, 1657, 1777, 1811, 2027, 2069, 2129, 2179, 2503, 2549, 2609, 2657

Offset: 0

Clark Kimberling, Nov 20 2024

nonn

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

Cf. A000040, A013636, A151800, A378136, A378137.

Table[NextPrime[n*NextPrime[n]], {n, 1, 80}]

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

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

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

cp's OEIS Frontend

A378135 a(n) = p(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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Formula

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

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