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A219790
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Smallest prime not neighboring a prime(n)-smooth number.
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1
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11, 29, 43, 67, 103, 137, 173, 173, 173, 283, 283, 283, 283, 283, 317, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 787, 787, 787, 907, 907, 907, 907, 1433, 1433, 1433, 1433, 1433, 1447, 1543, 1543, 1867, 1867, 1867, 1867, 1867, 1867
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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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.
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
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
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.
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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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