A115564 Least number d such that 10^n -/+ d form a prime pair.

3, 3, 9, 69, 129, 39, 261, 213, 459, 33, 57, 39, 267, 657, 357, 1377, 3, 387, 1899, 393, 213, 651, 3273, 2733, 3423, 1533, 429, 603, 1131, 1137, 1113, 1131, 249, 603, 2979, 159, 429, 921, 1269, 2757, 777, 789, 2277, 11799, 9, 5343, 1821, 6981, 23049, 1623

Offset: 1

Author

Lekraj Beedassy, Mar 11 2006

Keywords

• nonn
• changed

Comments

a(n) == 0 (mod 3). - Robert G. Wilson v, Mar 13 2006

Examples

			a(1)=3 because 10-3=7 and 10+3=13 both of which are primes.
a(3)=9 because 1000-9=991 and 1000+9=1009 both of which are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..422

Crossrefs

Cf. A082467, A113213, A117738.

Programs

Maple

f:= proc(n) local k;
for k from 3 by 6 do
    if isprime(10^n+k) and isprime(10^n-k) then return k fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, May 25 2018

Mathematica

f[n_] := Block[{k = 1}, While[ ! PrimeQ[10^n - 3k] || ! PrimeQ[10^n + 3k], k++ ]; 3k]; Array[f, 50]
dpp[n_]:=Module[{n10=10^n,np=NextPrime[10^n],diff},diff=np-n10; While[ !PrimeQ[n10-diff],np=NextPrime[np];diff=np-n10];np-n10]; Array[dpp,80] (* Harvey P. Dale, Mar 28 2012 *)

PARI

{ for (n = 1, 80, tenp = 10^n ; p = nextprime(tenp) ; while ( p-tenp < tenp, diff=p-tenp ; if ( isprime(tenp-diff), print1(diff",") ; break ; ) ; p=nextprime(p+1) ; ) ; ) } \\ R. J. Mathar, Mar 15 2006

Formula

a(n) = 3*A117738(n) = A082467(10^n). - Robert Israel, May 25 2018

Extensions

More terms from Craig Baribault (csb166(AT)psu.edu) and Robert G. Wilson v, Mar 13 2006

More terms from R. J. Mathar, Mar 15 2006

Corrected by Harvey P. Dale, Mar 28 2012