A358656 -id:A358656 - cp's OEIS frontend

A358979 Least prime p such that p^n + 4 is the product of n distinct primes.

3, 19, 11, 29, 131, 631, 983, 353, 9941, 20089, 15031, 8387, 102931

Offset: 1

J.W.L. (Jan) Eerland, Dec 27 2022

Corresponding values of p^n + 4 are 7, 365, 707285, 38579489655, 63121332085847285, 886899938586555644331, 241100240228887100165, ...

If they exist, a(14) > 106123, a(15) > 41257, a(16) > 31567.

			a(1) = 3; 3^1 + 4 = 7.
a(2) = 19; 19^2 + 4 = 5 * 73.
a(3) = 11; 11^3 + 4 = 3 * 5 * 89.
a(4) = 29; 29^4 + 4 = 5 * 17 * 53 * 157.

Cf. A358656, A280005, A000961, A005117.

Table[b=4;y[a_]:=FactorInteger[Prime[a]^n+b];k=1;Monitor[Parallelize[While[True,If[And[Length[y[k]]==n,Count[Flatten[y[k]],1]==n],Break[]];k++];k],k]//Prime,{n,1,10}]

a(n) = forprime(p=2, , my(f=factor(p^n + 4)); if (issquarefree(f) && (omega(f) == n), return(p)));

A363585 Least prime p such that p^n + 6 is the product of n distinct primes.

Original entry on oeis.org

5, 2, 23, 127, 71, 353, 1279, 3851, 3049, 18913, 47129, 352073, 696809

Offset: 1

J.W.L. (Jan) Eerland, Jun 10 2023

Corresponding values of p^n + 6 are 11, 10, 12173, 260144647, 1804229357, 1934854145598535, 5598785270206921122565, ...

Upper bounds for the next terms are a(12) <= 352073, a(13) <= 696809, a(14) <= 1496423. - Hugo Pfoertner, Jun 11 2023

			a(1) = 5; 5^1 + 6 = 11.
a(2) = 2; 2^2 + 6 = 2 * 5.
a(3) = 23; 23^3 + 6 = 7 * 37 * 47.
a(4) = 127; 127^4 + 6 = 7 * 131 * 367 * 773.

Cf. A000961, A001221, A005117, A280005, A358656, A362957.

Table[b=6;y[a_]:=FactorInteger[Prime[a]^n+b];k=1;Monitor[Parallelize[While[True,If[And[Length[y[k]]==n,Count[Flatten[y[k]],1]==n],Break[]];k++];k],k]//Prime,{n,1,10}]

a(n) = forprime(p=2, , my(f=factor(p^n + 6)); if (issquarefree(f) && (omega(f) == n), return(p)));

a(11) from Hugo Pfoertner, Jun 11 2023
a(12) from J.W.L. (Jan) Eerland, Jan 07 2024
a(13) from Hugo Pfoertner, confirmed by Daniel Suteu, Feb 10 2024

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A358979 Least prime p such that p^n + 4 is the product of n distinct primes.

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