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 A219697 Primes neighboring a 7-smooth number. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 *) 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

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Last modified June 13 15:33 EDT 2021. Contains 345008 sequences. (Running on oeis4.)