cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 20 2024

Keywords

Examples

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

Crossrefs

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

Programs

  • Mathematica
    Table[NextPrime[n*NextPrime[n]], {n, 1, 80}]
  • PARI
    p(n) = nextprime(n+1);
a(n) = p(n*p(n)); \\ Michel Marcus, Nov 21 2024

Formula

a(n) = A151800(n*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

Views

Author

Clark Kimberling, Jan 18 2025

Keywords

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    Table[NextPrime[(n+1)*NextPrime[n]], {n, 0, 80}]
  • PARI
    p(n) = nextprime(n+1);
a(n) = p((n+1)*p(n)); \\ Michel Marcus, Jan 18 2025
  • Python
    from sympy import nextprime
def A379405(n): return nextprime((n+1)*nextprime(n)) # Chai Wah Wu, Jan 20 2025

Formula

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

A380657 Numbers whose prime factorization has more Pythagorean prime factors than non-Pythagorean prime factors (including multiplicities).

Original entry on oeis.org

5, 13, 17, 25, 29, 37, 41, 50, 53, 61, 65, 73, 75, 85, 89, 97, 101, 109, 113, 125, 130, 137, 145, 149, 157, 169, 170, 173, 175, 181, 185, 193, 195, 197, 205, 221, 229, 233, 241, 250, 255, 257, 265, 269, 275, 277, 281, 289, 290, 293, 305, 313, 317, 325, 337
Offset: 1

Views

Author

Clark Kimberling, Jan 30 2025

Keywords

Examples

			50 appears because 2*5*5 has 2 Pythagorean prime factors but only 1 non-Pythagorean prime factor.

Crossrefs

Cf. A000040, A002144, A002145, A083025, A376961, A377625, A378137, A378139, A378140.

Programs

  • Mathematica
    f[{x_, y_}] := If[Mod[x, 4] == 1, y, -y];
s[n_] := Map[f, FactorInteger[n]];
p[n_] := {Total[Select[s[n], # > 0 &]], -Total[Select[s[n], # < 0 &]]};
p[1] = {0, 0};
t = Table[p[n], {n, 1, 500}];
u = Map[First, t];  (* A083025 *)
v = Map[Last, t] ;  (* A376961 *)
v - u (* A377625 *);
Flatten[Position[v - u, -1]]  (* this sequence *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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