OFFSET
1,1
COMMENTS
Subsequence of A020472. The primes generated from the subtractions are in A020469, A020458, and A020449, respectively. Final digits are necessarily 9 (here), then 7, 3, and 1. Because leading 8's are permitted in the terms here, the primes generated by subtracting 8's may have fewer digits than the others.
LINKS
Robert Israel, Table of n, a(n) for n = 1..1188
EXAMPLE
9898898899 is prime and so are 7676676677, 3232232233, and 1010010011, so it is a term. Although 9349, 9349-2222=7127, 9349-6666=2683, and 9349-8888=461 are four primes, 9349 is not a term as subtracting 6 or 8 from the digits 3 and 4 is not possible (no "borrowing" is permitted).
MAPLE
Res:= NULL: count:= 0:
for d from 2 while count < 100 do
v:= (10^d-1)/9;
for m from 1 to d do
if m mod 3 <> 0 and 2*d+m mod 3 <> 0 then
for S in combinat:-choose([$1..(d-2)], m-1) do
q:= 1+add(10^i, i=S);
if andmap(isprime, [q, 2*v+q, 6*v+q, 8*v+q]) then
count:= count+1; Res:= Res, 8*v+q;
fi
od;
fi
od;
od:
sort([Res]); # Robert Israel, Nov 14 2022
MATHEMATICA
okQ[n_]:=Module[{idn=IntegerDigits[n]}, And@@PrimeQ[FromDigits/@ {idn-2, idn-6, idn-8}]]; Select[Flatten[Table[Select[FromDigits/@ Tuples[ {8, 9}, n], PrimeQ], {n, 18}]], okQ] (* Harvey P. Dale, Jul 27 2011 *)
PROG
(PARI) {/* Program based on that of M. F. Hasler in A020472. */
for(nd=1, 20, p=vector(nd, i, 10^(nd-i))~; r=(10^nd-1)/9;
forvec(v=vector(nd, i, [8+(i==nd), 9]), q=v*p; isprime(q) &&
isprime(q-2*r ) && isprime(q-6*r ) && isprime(q-8*r ) && print1(q", ")))}
(Python)
from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
for d in count(2):
subs = list(map(int, ["2"*d, "6"*d, "8"*d]))
for first in product("89", repeat=d-1):
t = int("".join(first) + "9")
if isprime(t) and all(isprime(t-s) for s in subs): yield t
print(list(islice(agen(), 15))) # Michael S. Branicky, Nov 15 2022
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Rick L. Shepherd, Mar 30 2010
STATUS
approved