A052902 Take n-th prime p, let P = all primes that can be obtained by permuting the digits of p and possibly omitting zeros; a(n) = |p-q| where q in P is the closest to p but different from p (a(n)=0 if no such q exists).

0, 0, 0, 0, 0, 18, 54, 0, 0, 0, 18, 36, 0, 0, 0, 0, 0, 0, 0, 54, 36, 18, 0, 0, 18, 90, 72, 36, 90, 18, 144, 18, 36, 54, 270, 0, 414, 450, 450, 36, 18, 630, 720, 54, 18, 720, 0, 0, 0, 0, 0, 54, 180, 270, 0, 0, 0, 144, 450, 540, 540, 54, 234, 180, 18, 144, 18, 36, 396, 90, 0, 234, 306

Offset: 1

Author

N. J. A. Sloane, Mar 16 2000

Keywords

• base
• easy
• nonn

Examples

			a(6)=18 since 6th prime is 13 and 31-13=18. a(25)=90 since 23rd prime is 101 and 101-11=90.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A052998, A052999, A053544, A052495.

Programs

Mathematica

pdp[n_]:=Module[{p1=FromDigits/@Permutations[IntegerDigits[n]],p2=FromDigits/@ Permutations[ Select[IntegerDigits[n],#>0&]],p3},p3=Select[ Union[ Join[ p1,p2]],PrimeQ[#]&&#!=n&];If[Length[p3]==0,0,First[Abs[Nearest[p3,n]-n]]]]; Table[pdp[n],{n,Prime[Range[80]]}] (* Harvey P. Dale, Nov 11 2016 *)

Extensions

More terms from Asher Auel, May 12 2000