A327133 The difference between 10^n and the lesser of the twin primes immediately before.

5, 29, 119, 71, 11, 41, 29, 413, 809, 299, 239, 41, 1511, 29, 2033, 359, 1193, 1073, 1499, 2261, 5003, 2429, 1793, 4331, 833, 5879, 359, 779, 2813, 1061, 2099, 1811, 3281, 5201, 533, 5483, 1679, 1421, 26801, 12089, 2843, 27773, 9641, 10841, 4763, 2129, 1019, 20531, 8519, 14339

Offset

1,1

Comments

All terms are congruent to 5 (mod 6).

Records: 5, 29, 119, 413, 809, 1511, 2033, 2261, 5003, 5879, 26801, ..., 37058441, ... - Robert G. Wilson v, Dec 10 2019

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1250

Formula

a(n) = A011557(n) - A092250(n).

Example

a(1) = 5 because the greatest twin prime pair less than 10 is {5, 7};
a(2) = 29 since the greatest 2-digit twin prime pair is {71, 73};
a(3) = 119 since the greatest 3-digit twin prime pair is {881, 883}; etc.

Maple

f:= proc(n) local w, p, q;
w:= 10^n; q:= w;
do
  p:= q;
  q:= prevprime(p);
  if p-q = 2 then return w-q fi;
od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 28 2019

Mathematica

p[n_] := Block[{d = PowerMod[10, n, 6]}, 10^n - NestWhile[# -6 &, 10^n -d -1, !PrimeQ[#] || !PrimeQ[# +2] &]]; Array[p, 50] (* updated Nov 29 2019 *)

Prog

(PARI) prectwin(n)=n++; while(!isprime(2+n=precprime(n-1)), ); n
a(n)=10^n - prectwin(10^n) \\ Charles R Greathouse IV, Nov 28 2019

Crossrefs

Cf. A011557, A092250.

Sequence in context: A297632 A153077 A000352 * A267921 A241676 A291889

Adjacent sequences: A327130 A327131 A327132 * A327134 A327135 A327136

Keyword

nonn

Author

Robert G. Wilson v, Nov 28 2019

Status

approved