A321796 Prime p such that the prime before p is a substring of p^3.

3, 17, 31, 59, 997, 2837, 57349, 83773, 224813, 861743, 9999991, 61879669, 95895673, 763137931, 1463016067, 1608398527, 6909512173, 38095693807, 94041857089, 4913845865567

Offset: 1

Author

Paolo P. Lava, Nov 19 2018

Keywords

• nonn
• base
• more

Comments

10^18-11 and 10^31-27 are also terms. - Giovanni Resta, Nov 20 2018

Examples

			Prime before 3 is 2 and it is a substring of 3^3 = 27.
		

Crossrefs

Cf. A052075.

Programs

Maple

P:=proc(q) local a,n; for n from 2 to q do a:=ithprime(n);
if searchtext(convert(prevprime(a),string),convert(a^3,string))>0
then print(a); fi; od; end: P(10^5);

Mathematica

sub[x_, y_] := StringPosition @@ ToString /@ {x, y} != {}; p = Prime@ Range@ 100000; p[[Select[Range[2, 100000], sub[p[[#]]^3, p[[# - 1]]] &]]] (* Giovanni Resta, Nov 20 2018 *)
Select[Prime[Range[700000]],SequenceCount[IntegerDigits[#^3],IntegerDigits[ NextPrime[ #,-1]]]>0&] (* The program generates the first 11 terms of the sequence; to generate all terms, increase the Range constant to 174344399360 but the program will take an extremely long time to run. *) (* Harvey P. Dale, Mar 27 2020 *)

Python

from itertools import count, islice
from sympy import prevprime, prime
def A321796_gen(): return filter(lambda p: str(prevprime(p)) in str(p**3), (prime(n) for n in count(2)))
A321796_list = list(islice(A321796_gen(),5)) # Chai Wah Wu, Jan 20 2022

Extensions

a(10)-a(20) from Giovanni Resta, Nov 20 2018