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A052902
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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).
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7
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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
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OFFSET
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1,6
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LINKS
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EXAMPLE
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a(6)=18 since 6th prime is 13 and 31-13=18. a(25)=90 since 23rd prime is 101 and 101-11=90.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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