

A219697


Primes neighboring a 7smooth 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
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OFFSET

1,1


COMMENTS

This is to the 7smooth numbers A002473 as A219528 is to the 3smooth numbers A003586 and as A219669 is to the 5smooth numbers A051037. The first primes NOT within one of a 7smooth 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 231 = 22 = 2 * 11 and 23+1 = 24 = 2^3 * 3 is 7smooth 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



