A278698 Primes p such that every suffix of the base-5 representation of p is either a prime or 1.

2, 3, 7, 11, 13, 17, 23, 53, 61, 67, 73, 101, 103, 107, 113, 127, 251, 257, 263, 311, 317, 353, 503, 523, 601, 607, 613, 1303, 1567, 1753, 1877, 2503, 3023, 6257, 6263, 6311, 6317, 6323, 6353, 6857, 6863, 7817, 8753, 9377, 12503, 12511, 12517, 12553, 12601, 12613, 12757

Offset: 1

Author

Randy L. Ekl, Nov 26 2016

Keywords

• nonn
• base

Examples

			61=221_5 is in the sequence since it is a prime and each of its base-5 suffixes (21_5=11 and 1_5=1) is either prime or 1.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A143390, A278697.

Programs

PARI

expand(v,d)=my(u=List(v), D=5^d); forstep(x=D,4*D,D, for(i=1,#v, if(isprime(t=x+v[i]), listput(u,t)))); Vec(u)
list(lim)=my(v=[1,2,3]); for(n=1,#digits(lim\=1,5)-1, v=expand(v,n)); select(k->k<=lim && k>1, v) \\ Charles R Greathouse IV, Nov 26 2016

PARI

isok(n) = {if (isprime(n), pp = 5^logint(n, 5); while ((isprime(rem=(n % pp)) || (rem == 1)) && (pp != 1), pp = pp/5); pp == 1;);} \\ Michel Marcus, Nov 26 2016