A052075 Primes p such that nextprime(p) is substring of p^3.

11, 101, 2239, 34297, 43789, 53549, 535487, 59897017, 430784719, 2549592677, 2837138669, 97969345967, 100000000019, 328096840219, 4110739763869

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base
• more
• nice

Comments

a(16) > 6.9*10^12. - Giovanni Resta, Jul 02 2018

Crossrefs

Cf. A052076, A052073, A052074.

Programs

Mathematica

Select[Prime[Range[1,10000]],StringContainsQ[ToString[#^3],ToString[NextPrime[#]]]&] (* Julien Kluge, Sep 19 2016 *)
Select[Prime[Range[45000]],SequenceCount[IntegerDigits[#^3],IntegerDigits[ NextPrime[ #]]]>0&] (* Requires Mathematica version 10 or later *) (* The program generates the first 7 terms of the sequence: to generate more, increase Range constant. *) (* Harvey P. Dale, Jan 25 2021 *)

Python

from itertools import count, islice
from sympy import prime, nextprime
def A052075_gen(): return filter(lambda p: str(nextprime(p)) in str(p**3), (prime(n) for n in count(1)))
A052075_list = list(islice(A052075_gen(),3)) # Chai Wah Wu, Jan 20 2022

Extensions

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006

Offset corrected by N. J. A. Sloane, Jul 13 2016

a(12)-a(15) from Giovanni Resta, Jul 02 2018

Definition clarified by Chai Wah Wu, Jan 20 2022