A347977 Primes of the form 2^p * 3^q * 5^r * 7^s - 1.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 53, 59, 71, 79, 83, 89, 97, 107, 127, 139, 149, 167, 179, 191, 199, 223, 239, 251, 269, 293, 349, 359, 383, 419, 431, 449, 479, 499, 503, 587, 599, 647, 719, 809, 839, 863, 881, 971, 1049, 1151, 1249, 1259, 1279, 1399, 1439, 1499, 1511, 1567, 1619, 1889

Offset

1,1

Comments

Restricting to r = s = 0 gives A005105; s = 0 gives A293194.

Primes of the form A002473(k) - 1.

Links

Flávio V. Fernandes, Table of n, a(n) for n = 1..10000

Example

251 = 2^2 * 3^2 * 5^0 * 7^1 - 1 and 839 = 2^3 * 3^1 * 5^1 * 7^1 - 1 are terms.

Mathematica

With[{n = 2000}, Sort@ Select[Flatten@ Table[2^p * 3^q * 5^r * 7^s - 1, {p, 0, Log[2, n]}, {q, 0, Log[3, n/(2^p)]}, {r, 0, Log[5, n/(2^p * 3^q)]}, {s, 0, Log[7, n/(2^p * 3^q * 5^r)]}], PrimeQ]] (* Amiram Eldar, Sep 25 2021 after Michael De Vlieger at A293194 *)

Prog

(PARI) isok(p) = isprime(p) && (vecmax(factor(p+1)[, 1]) < 11); \\ Michel Marcus, Nov 10 2021
(PARI) upto(limit)={my(P=[2, 3, 5, 7]); local(L=List()); my(recurse(k, t) = if(t<=limit+1, if(k>#P, if(isprime(t-1), listput(L, t-1)), my(b=P[k]); for(e=0, logint(limit+1, b), self()(k+1, t*b^e))))); recurse(1, 1); vecsort(Vec(L))} \\ Andrew Howroyd, Nov 20 2021

Crossrefs

Cf. A002473, A005105, A293194.

Sequence in context: A171045 A222566 A299171 * A002267 A178762 A051750

Adjacent sequences: A347974 A347975 A347976 * A347978 A347979 A347980

Keyword

nonn

Author

Flávio V. Fernandes, Sep 21 2021

Status

approved