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.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A342798 A342799 A342800 * A342802 A342803 A342804

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Mar 21 2021

Status

approved