cp's OEIS Frontend

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).

%I A052999 #12 Jul 02 2025 19:59:22
%S A052999 0,0,0,0,90,18,54,90,1980,199980,18,36,360,3960,3960,450,450,540,540,
%T A052999 36,36,18,79999999999999999999999999999920,720,18,90,72,36,90,18,144,
%U A052999 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
%N 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).
%C A052999 Conjecture: a(n) > 0 for n > 4. - _Sean A. Irvine_, Nov 23 2021
%e A052999 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.
%e A052999 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
%Y A052999 Cf. A052902, A052998, A053544, A052495, A052484.
%K A052999 base,easy,nonn
%O A052999 1,5
%A A052999 _N. J. A. Sloane_, Mar 16 2000
%E A052999 More terms from _Asher Auel_, May 12 2000
%E A052999 a(23) corrected by _Sean A. Irvine_, Nov 23 2021