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%I #15 Apr 19 2021 17:26:22
%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,71,73,79,83,89,97,
%T 101,107,109,113,127,139,149,151,163,167,179,181,191,193,197,199,211,
%U 223,239,241,251,257,269,271,281,293,337,349,359,379,383,401,419,421,431
%N Primes neighboring a 7-smooth number.
%C 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, ...
%H David A. Corneth, <a href="/A219697/b219697.txt">Table of n, a(n) for n = 1..10765</a> (terms <= 10^16)
%F Primes INTERSECTION {2^h 3^i 5^j 7^k +/-1 for h,i,j,k >= 0}.
%e 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
%t 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 *)
%o (PARI) is7smooth(n) = forprime(p = 2, 7, n /= p^valuation(n, p)); n==1
%o is(n) = isprime(n) && (is7smooth(n - 1) || is7smooth(n + 1)) \\ _David A. Corneth_, Apr 19 2021
%Y Cf. A000040, A002473, A051037, A080194, A219528.
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Nov 25 2012
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