A052999 - OEIS

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).

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

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OFFSET

1,5

COMMENTS

Conjecture: a(n) > 0 for n > 4. - Sean A. Irvine, Nov 23 2021

LINKS

Table of n, a(n) for n=1..58.

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

Cf. A052902, A052998, A053544, A052495, A052484.