A284292 Primes containing a digit 8.

83, 89, 181, 281, 283, 383, 389, 487, 587, 683, 787, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 983, 1087, 1181, 1187, 1283, 1289, 1381, 1481, 1483, 1487, 1489, 1583, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867

Offset: 1

Author

Jaroslav Krizek, Mar 25 2017

Keywords

• nonn
• base

Comments

Subsequence of A011538 and A062677.

Differs from A062677 which contains also the composites 6889 = 83^2, 7387 = 83*89, 23489=83*283, 25187=89*283, 31789 = 83*383 etc. - R. J. Mathar, Mar 27 2017

Links

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

Crossrefs

Cf. Primes containing a digit k for k = 0 - 9: A056709 (k = 0), A208270 (k = 1), A208272 (k = 2), A212525 (k = 3), A284290 (k = 4), A257667 (k = 5), A284291 (k = 6), A257668 (k = 7), this sequence (k = 8), A106093 (k = 9).

Programs

Magma

[p: p in PrimesUpTo(10000) | 8 in Intseq(p)];

Maple

isA284292 := proc(n)
    if isprime(n) then
        convert(convert(n,base,10),set) ;
        if 8 in % then
            true;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 1 to 2000 do
    if isA284292(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Mar 27 2017

Mathematica

Select[Prime@ Range@ 500, MemberQ[ IntegerDigits@ #, 8] &] (* Giovanni Resta, Mar 25 2017 *)

Python

from sympy import primerange
print([n for n in primerange(2, 2000) if '8' in str(n)]) # Indranil Ghosh, Mar 25 2017