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

1,1

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A082467, A113213, A117738.

Sequence in context: A216147 A334774 A257627 * A122961 A165421 A227432

Adjacent sequences: A115561 A115562 A115563 * A115565 A115566 A115567

Keyword

nonn

Author

Lekraj Beedassy, Mar 11 2006

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

Status

approved