login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A255669
Primes p such that p divides the concatenation of the next two primes.
0
3, 7, 61, 167
OFFSET
1,1
COMMENTS
No additional terms up to the 5-millionth prime. Is the sequence finite and complete?
No additional terms up to the billionth prime. - Chai Wah Wu, Mar 10 2015
a(5) > 10^18. If the reasonable assumption nextprime(p) < p + (log p)^2 holds, then a(5) > 10^53. However, the 192-digits prime
7046979865771812080536912751677852348993288590604026845637583892...
6174496644295302013422818791946308724832214765100671140939597315...
4362416107382550335570469798657718120805369127516778523489932887 is in the sequence. - Giovanni Resta, May 08 2015
EXAMPLE
The three primes beginning with 61 are 61, 67, and 71, and 61 evenly divides 6771.
MATHEMATICA
divQ[{a_, b_, c_}]:=Divisible[FromDigits[Flatten[IntegerDigits/@{b, c}]], a]; Transpose[Select[Partition[Prime[Range[500]], 3, 1], divQ]][[1]]
PROG
(Python)
from sympy import nextprime
A255669_list, p1, p2, l = [], 2, 3, 10
for n in range(10**8):
....p3 = nextprime(p2)
....if p3 >= l: # this test is sufficient by Bertrand-Chebyshev theorem
........l *= 10
....if not ((p2 % p1)*l + p3) % p1:
........A255669_list.append(p1)
....p1, p2 = p2, p3 # Chai Wah Wu, Mar 09 2015
CROSSREFS
Sequence in context: A084289 A183174 A329966 * A258184 A362347 A077703
KEYWORD
nonn,base
AUTHOR
Harvey P. Dale, Mar 01 2015
STATUS
approved