A357935 Primes p such that the sum of digits of 11*p is 11.

19, 37, 73, 919, 937, 991, 1873, 2791, 3637, 3673, 3691, 4591, 6373, 8191, 91837, 91873, 92737, 92791, 93637, 94573, 181837, 181873, 181891, 182773, 183637, 183691, 185491, 186391, 187273, 272737, 274591, 275491, 276373, 277273, 278191, 363691, 365473, 367273, 455473, 455491, 458191, 459091

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 21 2022

Keywords

• nonn
• base

Comments

Primes in A279771.

All terms == 1 (mod 18).

Includes (8*10^k+3)/11 for k = 2, 6, 60, 320, 600. Any others?

Examples

			a(3) = 73 is a term because 73 is prime and 11*73 = 803 with 8+0+3 = 11.
		

Links

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

Crossrefs

Cf. A166311, A279771.

Programs

Maple

filter:= proc(p) convert(convert(11*p,base,10),`+`) = 11 and isprime(p):
select(filter, [seq(i,i=1..10^6,18)]);

Mathematica

Select[Prime[Range[40000]], Plus @@ IntegerDigits[11*#] == 11 &] (* Amiram Eldar, Oct 21 2022 *)