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

Author

Jonathan Vos Post, Nov 25 2012

Keywords

• nonn
• easy

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, ...

Examples

			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
		

Links

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

Crossrefs

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

Programs

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 *)

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

Formula

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