A163001 a(n) = the number of integers k, 1 <= k <= n-1, such that p(n)-p(k) is divisible by n-k (here p(n) = the n-th prime.)

0, 1, 1, 2, 2, 2, 3, 3, 4, 5, 3, 4, 5, 5, 5, 7, 4, 7, 5, 5, 9, 6, 7, 3, 6, 5, 5, 3, 5, 5, 6, 6, 8, 6, 5, 7, 9, 6, 8, 5, 5, 7, 7, 6, 9, 6, 7, 9, 8, 7, 4, 7, 8, 4, 7, 7, 7, 5, 7, 4, 6, 5, 6, 9, 6, 5, 8, 10, 11, 10, 11, 12, 12, 11, 10, 12, 12, 13, 13, 13, 9, 14, 10, 15, 17, 16, 16, 18, 17, 9, 5, 18, 20

Offset

1,4

Links

Table of n, a(n) for n=1..93.

Example

The 10th prime is 29. Checking: 29-2=27 is divisible by 10-1=9. 29-3=26 is not divisible by 10-2=8. 29-5=24 is not divisible by 10-3=7. 29-7=22 is not divisible by 10-4=6. 29-11=18 is not divisible by 10-5=5. 29-13=16 is divisible by 10-6=4. 29-17=12 is divisible by 10-7=3. 29-19=10 is divisible by 10-8=2. And 29-23=6 is divisible by 10-9=1. There are therefore five k's where p(10)-p(k) is divisible by 10-k. So a(10)=5.

Maple

a := proc (n) local ct, k: ct := 0: for k to n-1 do if `mod`(ithprime(n)-ithprime(k), n-k) = 0 then ct := ct+1 else end if end do: ct end proc: seq(a(n), n = 1 .. 100); # Emeric Deutsch, Jul 30 2009
A163001 := proc(n) local a, k ; a := 0 ; for k from 1 to n-1 do if ( ithprime(n)-ithprime(k) ) mod (n-k) = 0 then a := a+1; fi; od: a ; end ; seq(A163001(n), n=1..120) ; # R. J. Mathar, Jul 30 2009

Crossrefs

Sequence in context: A240868 A029149 A080570 * A239913 A323701 A226591

Adjacent sequences: A162998 A162999 A163000 * A163002 A163003 A163004

Keyword

nonn

Author

Leroy Quet, Jul 20 2009

Extensions

Extended by Emeric Deutsch and R. J. Mathar, Jul 30 2009

Status

approved