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

1,1

Comments

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

Links

Table of n, a(n) for n=1..15.

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 *)

Prog

(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

Crossrefs

Cf. A052076, A052073, A052074.

Sequence in context: A088292 A135563 A233432 * A070854 A075767 A292014

Adjacent sequences: A052072 A052073 A052074 * A052076 A052077 A052078

Keyword

nonn,base,more,nice

Author

Patrick De Geest, Jan 15 2000

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

Status

approved