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A342801
Primes p such that, if b is the sum of digits of p, y = p mod b and x = (p-y)/b, then p-x*y, p+x*y, x+y and x-y are all prime.
1
127, 173, 181, 257, 281, 359, 563, 569, 577, 719, 751, 1061, 1381, 1879, 1901, 4327, 4759, 5441, 6397, 6977, 7207, 7933, 8387, 8419, 8521, 9349, 10009, 10891, 11311, 11443, 11467, 12323, 13567, 13873, 14369, 14929, 15299, 15683, 16073, 17351, 18041, 18749, 24407, 24481, 24767, 25819, 27067, 27739
OFFSET
1,1
LINKS
EXAMPLE
a(3) = 181 is a term because 181 is prime, with sum of digits b=10, y=1, x=18, and n-x*y=163, n+x*y=199, x+y=19, and x-y=17 are all prime.
MAPLE
filter:= proc(n) local b, x, y;
if not isprime(n) then return false fi;
b:= convert(convert(n, base, 10), `+`);
if b <= 1 then return false fi;
y:= n mod b;
x:= (n-y)/b;
isprime(n-x*y) and isprime(n+x*y) and isprime(x+y) and isprime(x-y)
end proc:
select(filter, [2, seq(i, i=3..10^5, 2)]);
CROSSREFS
Sequence in context: A094933 A156702 A180536 * A137985 A065092 A141916
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Mar 21 2021
STATUS
approved