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A052999
Take n-th prime p, let P(p) = all primes that can be obtained by permuting the digits of p and possibly adding or omitting zeros; a(n) = |p-q| where q in P(p) is the closest to p but different from p (a(n)=0 if no such q exists).
5
0, 0, 0, 0, 90, 18, 54, 90, 1980, 199980, 18, 36, 360, 3960, 3960, 450, 450, 540, 540, 36, 36, 18, 79999999999999999999999999999920, 720, 18, 90, 72, 36, 90, 18, 144, 18, 36, 54, 270, 900, 414, 450, 450, 36, 18, 630, 720, 54, 18, 720, 810, 1980, 1800, 1800, 2790, 54, 180, 270, 20250, 1800, 1800, 144
OFFSET
1,5
COMMENTS
Conjecture: a(n) > 0 for n > 4. - Sean A. Irvine, Nov 23 2021
EXAMPLE
a(6)=18 since 6th prime is 13 and 31-13=18. a(9)=1980 because 9th prime is 23 and the smallest prime in P(6) different from 23 is 2003; 2003-23=1980.
a(23)=(8*10^31+3)-83 because 8*10^31+3 is closest prime distinct from 83 but in P(83). - Sean A. Irvine, Nov 23 2021
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
N. J. A. Sloane, Mar 16 2000
EXTENSIONS
More terms from Asher Auel, May 12, 2000
a(23) corrected by Sean A. Irvine, Nov 23 2021
STATUS
approved