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%I #21 May 13 2013 01:54:23
%S 11,29,43,67,103,137,173,173,173,283,283,283,283,283,317,653,653,653,
%T 653,653,653,653,653,653,653,653,653,653,787,787,787,907,907,907,907,
%U 1433,1433,1433,1433,1433,1447,1543,1543,1867,1867,1867,1867,1867,1867
%N Smallest prime not neighboring a prime(n)-smooth number.
%H Charles R Greathouse IV, <a href="/A219790/b219790.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) > 6p for n > 1, where p is the n-th prime. - _Charles R Greathouse IV_, Nov 28 2012
%e a(2) = 29, the smallest prime not neighboring a 3-smooth number, since 3 is the 2nd prime; i.e., not of the form 2^j*3^k +/- 1. 43-1 = 2*3*7, 43+1 = 2*2*11, so neither are 5-smooth.
%e a(3) = 43, the smallest prime not neighboring a 5-smooth number, since 5 is the 3rd prime, and 43-1 = 42 = 2 * 3 * 7 is not 5 smooth, and 43+1 = 44 = 2^2 * 11 is not 5 smooth. - corrected by _Jason Kimberley_, Nov 29 2012
%e a(4) = 67, the smallest prime not neighboring a 7-smooth number, since 7 is the 4th prime, and 67-1 = 66 = 2 * 3 * 11 is not 7 smooth, and 67+1 = 68 = 2^2 * 17 is not 7 smooth. - corrected by _Jason Kimberley_, Nov 29 2012
%e a(5) = 103, the smallest prime not neighboring a 11-smooth number, since 11 is the 5th prime, and 103-1 = 102 = 2 * 3 * 17 is not 11 smooth, and 103+1 = 104 = 2^3 * 13 is not 11 smooth.
%e a(6) = 137, the smallest prime not neighboring a 13-smooth number, since 13 is the 6th prime, and 137-1 = 136 = 2^3 * 17 is not 13 smooth, and 137+1 = 138 = 2 * 3 * 23 is not 13 smooth.
%o (PARI) a(n)=my(p=prime(n));forprime(q=6*p-1,,if(vecmax(factor(q-1)[,1])>p && vecmax(factor(q+1)[,1])>p,return(q))) \\ _Charles R Greathouse IV_, Nov 28 2012
%Y Cf. A000040, A002473, A051037, A051038, A080194, A219528, A219697, A219785.
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Nov 27 2012
%E a(3) and a(4) corrected by _Charles R Greathouse IV_, Nov 28 2012
%E a(1) and a(7)-a(53) from _Charles R Greathouse IV_, Nov 28 2012
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