A053544 -id:A053544 - cp's OEIS frontend

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

N. J. A. Sloane, Mar 16 2000

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

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

Cf. A052998, A052999, A053544, A052495.

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 *)

More terms from Asher Auel, May 12 2000

A052495 Take n-th prime p, let P = all primes having same digits; a(n) = q-p where q is smallest prime in P >p if q exists; otherwise a(n) = p-r where r is largest prime in P

Original entry on oeis.org

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, 0, 0, 594, 0, 18, 144, 180, 36, 54, 270, 0, 414, 450, 450, 144, 18, 630, 720, 54, 522, 720, 0, 0, 0, 0, 0, 54, 180, 270, 0, 0, 0, 144, 450, 540, 540, 54, 0, 180, 18, 144, 18, 36, 396, 90, 0, 234

Offset: 1

Enoch Haga, Mar 16 2000

The primes in P are required to have the same number of digits as p; thus internal 0's must remain internal 0's.

			a(41)=18 because the 41st prime is 179. The primes having these digits are 179, 197, 719 and 971. The distance from 179 to 197 = 18.

Cf. A052902, A052998, A052999, A053544, A052494, A052507.

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).

Original entry on oeis.org

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

N. J. A. Sloane, Mar 16 2000

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

			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

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

More terms from Asher Auel, May 12 2000

a(23) corrected by Sean A. Irvine, Nov 23 2021

A052998 A052902 / 18.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 1, 5, 4, 2, 5, 1, 8, 1, 2, 3, 15, 0, 23, 25, 25, 2, 1, 35, 40, 3, 1, 40, 0, 0, 0, 0, 0, 3, 10, 15, 0, 0, 0, 8, 25, 30, 30, 3, 13, 10, 1, 8, 1, 2, 22, 5, 0, 13, 17, 2, 1, 0, 25, 1, 20, 0, 4, 10, 0, 0, 5, 0, 0, 5, 10, 10, 10, 26, 0, 4, 0

Offset: 1

N. J. A. Sloane, Mar 16 2000

Cf. A052902, A052999, A053544, A052495.

More terms from Asher Auel, May 12 2000

cp's OEIS Frontend

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).

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A052495 Take n-th prime p, let P = all primes having same digits; a(n) = q-p where q is smallest prime in P >p if q exists; otherwise a(n) = p-r where r is largest prime in P

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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).

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A052998 A052902 / 18.

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