|
|
A321796
|
|
Prime p such that the prime before p is a substring of p^3.
|
|
0
|
|
|
3, 17, 31, 59, 997, 2837, 57349, 83773, 224813, 861743, 9999991, 61879669, 95895673, 763137931, 1463016067, 1608398527, 6909512173, 38095693807, 94041857089, 4913845865567
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
Prime before 3 is 2 and it is a substring of 3^3 = 27.
|
|
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 *)
|
|
PROG
|
(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)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|