A219697 Primes neighboring a 7-smooth number.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, 97, 101, 107, 109, 113, 127, 139, 149, 151, 163, 167, 179, 181, 191, 193, 197, 199, 211, 223, 239, 241, 251, 257, 269, 271, 281, 293, 337, 349, 359, 379, 383, 401, 419, 421, 431

Offset

1,1

Comments

This is to the 7-smooth numbers A002473 as A219528 is to the 3-smooth numbers A003586 and as A219669 is to the 5-smooth numbers A051037. The first primes NOT within one of a 7-smooth number are 103, 131, 137, 157, 173, ...

Links

David A. Corneth, Table of n, a(n) for n = 1..10765 (terms <= 10^16)

Formula

Primes INTERSECTION {2^h 3^i 5^j 7^k +/-1 for h,i,j,k >= 0}.

Example

23 is in the sequence as one of 23-1 = 22 = 2 * 11 and 23+1 = 24 = 2^3 * 3 is 7-smooth and 23 is prime. - David A. Corneth, Apr 19 2021

Mathematica

mx = 2^10; t7 = Select[Sort[Flatten[Table[2^i * 3^j * 5^k * 7^l, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx]}, {k, 0, Log[5, mx]}, {l, 0, Log[7, mx]}]]], # <= mx &]; Union[Select[t7 + 1, PrimeQ], Select[t7 - 1, PrimeQ]] (* T. D. Noe, Nov 26 2012 *)
Select[Prime[Range[90]], Max[FactorInteger[#-1][[;; , 1]]]<11||Max[FactorInteger[#+1][[;; , 1]]]<11&] (* Harvey P. Dale, Nov 03 2024 *)

Prog

(PARI) is7smooth(n) = forprime(p = 2, 7, n /= p^valuation(n, p)); n==1
is(n) = isprime(n) && (is7smooth(n - 1) || is7smooth(n + 1)) \\ David A. Corneth, Apr 19 2021

Crossrefs

Cf. A000040, A002473, A051037, A080194, A219528.

Sequence in context: A234960 A118850 A322443 * A078668 A038614 A171047

Adjacent sequences: A219694 A219695 A219696 * A219698 A219699 A219700

Keyword

nonn,easy

Author

Jonathan Vos Post, Nov 25 2012

Status

approved