A341017 Primes p such that placing digit i at both ends of p produces another prime for at least two of i = [1,3,7, 9].

2, 5, 17, 23, 29, 31, 41, 43, 47, 53, 61, 67, 71, 73, 83, 101, 107, 113, 131, 149, 197, 239, 241, 257, 263, 269, 293, 317, 347, 359, 389, 401, 421, 431, 443, 503, 521, 557, 593, 599, 607, 641, 647, 677, 683, 701, 757, 797, 827, 887, 911, 953, 1031, 1103, 1109, 1117, 1171, 1181, 1187, 1223, 1277

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 02 2021

Keywords

• nonn
• base

Comments

Numbers that are in at least two of A069687, A069688, A069689 and A069690.

Examples

			a(3) = 17 is a term because 17 is in A069687 and A069689, i.e. 1171 and 7177 are prime.
		

Links

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

Crossrefs

Cf. A069687, A069688, A069689, A069690.

Programs

Maple

filter:= proc(n) local i; isprime(n) and numboccur(true,[seq(isprime(i+10*n+i*10^(2+ilog10(n))),i=[1,3,7,9])]) >= 2 end proc:
select(filter, [2,seq(i,i=3..1000)]);

Python

from sympy import isprime, nextprime
def ok(p): return sum(isprime(int(c+str(p)+c)) for c in "1379") >= 2
def aupto(limit): # only test primes
  alst, p = [], 2
  while p <= limit:
    if ok(p): alst.append(p)
    p = nextprime(p)
  return alst
print(aupto(1277)) #Michael S. Branicky, Feb 02 2021