

A219790


Smallest prime not neighboring a prime(n)smooth number.


1



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

1,1


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

a(n) > 6p for n > 1, where p is the nth prime.  Charles R Greathouse IV, Nov 28 2012


EXAMPLE

a(2) = 29, the smallest prime not neighboring a 3smooth number, since 3 is the 2nd prime; i.e., not of the form 2^j*3^k +/ 1. 431 = 2*3*7, 43+1 = 2*2*11, so neither are 5smooth.
a(3) = 43, the smallest prime not neighboring a 5smooth number, since 5 is the 3rd prime, and 431 = 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 7smooth number, since 7 is the 4th prime, and 671 = 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 11smooth number, since 11 is the 5th prime, and 1031 = 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 13smooth number, since 13 is the 6th prime, and 1371 = 136 = 2^3 * 17 is not 13 smooth, and 137+1 = 138 = 2 * 3 * 23 is not 13 smooth.


PROG

(PARI) a(n)=my(p=prime(n)); forprime(q=6*p1, , if(vecmax(factor(q1)[, 1])>p && vecmax(factor(q+1)[, 1])>p, return(q))) \\ Charles R Greathouse IV, Nov 28 2012


CROSSREFS

Cf. A000040, A002473, A051037, A051038, A080194, A219528, A219697, A219785.
Sequence in context: A156110 A155188 A045469 * A249436 A167521 A031338
Adjacent sequences: A219787 A219788 A219789 * A219791 A219792 A219793


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Nov 27 2012


EXTENSIONS

a(3) and a(4) corrected by Charles R Greathouse IV, Nov 28 2012
a(1) and a(7)a(53) from Charles R Greathouse IV, Nov 28 2012


STATUS

approved



