A052073
Primes p with the property that nextprime(p) is a substring of p^2.
Original entry on oeis.org
23, 83, 113, 1123, 200003, 328127, 381289, 714597769, 4916552822383
Offset: 1
381289 is a term because nextprime(381289) = 381301 is a substring of 381289^2 = 145381301521.
-
Select[Prime@Range[1000000],
StringContainsQ[ToString[#^2], ToString[NextPrime[#]]] &] (* Robert Price, Oct 12 2019 *)
a(8) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 04 2006
A052075
Primes p such that nextprime(p) is substring of p^3.
Original entry on oeis.org
11, 101, 2239, 34297, 43789, 53549, 535487, 59897017, 430784719, 2549592677, 2837138669, 97969345967, 100000000019, 328096840219, 4110739763869
Offset: 1
-
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 *)
-
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
More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006
A052076
List of cubes p^3 of primes with property that next prime after p is a substring of p^3.
Original entry on oeis.org
1331, 1030301, 11224377919, 40343019516073, 83964379378069, 153551511228149, 153548930496746303, 214889691497505989703913, 79943078473759892945966959, 16573430415736921632549592733, 22837138677705447754568672309, 940309072235302647342697969346063
Offset: 1
-
f[0]=8;f[n_]:=Module[{i=PrimePi[f[n-1]^(1/3)]+1},
While[StringPosition[ToString[Prime[i]^3],ToString[NextPrime[Prime[i]]]]=={}, i++];Prime[i]^3];f/@Range[7] (* Ivan N. Ianakiev, Nov 16 2016 *)
#^3&/@Select[Prime[Range[10^6]],SequenceCount[IntegerDigits[#^3],IntegerDigits[ NextPrime[ #]]]> 0&] (* Harvey P. Dale, Jul 29 2023 *)
More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006
A274932
Squares m = k^2 with the property that nextprime(k) is a substring of m.
Original entry on oeis.org
529, 729, 6889, 12769, 162409, 644809, 851929, 1261129, 47969476, 64048009, 317837584, 1600240009, 2822053129, 24421563076, 40001200009, 84290347584, 107667328129, 145381301521, 160002400009, 437766166321, 788815751409
Offset: 1
529 = 23^2, and nextprime(23) = 29 is a substring of 529, so 529 is a term.
-
Select[Range[2*10^6]^2,SequenceCount[IntegerDigits[#], IntegerDigits[ NextPrime[ Sqrt[ #]]]]>0&] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Jul 13 2016 *)
Select[Range[2*10^6], {} != StringPosition @@ ToString /@ {#^2, NextPrime@ #} &]^2 (* Giovanni Resta, Jul 15 2016 *)
A383607
Square array read by antidiagonals upwards: T(n,k) is the smallest k-digit prime p such that nextprime(p) is a substring of p^n; or -1 if no such prime exists, n>1, k>0.
Original entry on oeis.org
-1, -1, 23, -1, 11, 113, 2, 37, 101, 1123, 7, 17, 487, 2239, -1, 5, 47, -1, 5659, 34297, 200003, 3, 13, -1, 2399, 91801, 535487, -1, -1, 31, 607, 1279, 31627, 842483, -1, -1, 3, 41, 431, 3163, 12281, 825059, 6315629, 59897017, 714597769, -1, 37, 233, 1931, 15791, 179947, 5623421, -1, 430784719, -1
Offset: 2
T(2,3) = 113, because nextprime(113) = 127 is a substring in 113^2 = 12769, starting at position 1, and no smaller 3-digit prime satisfies this condition.
Top left corner begins at T(2,1):
-1, 23, 113, 1123, ...
-1, 11, 101, 2239, ...
-1, 37, 487, 5659, ...
2, 17, -1, 2399, ...
.., .., ..., ...., ...
-
T(n,k) = forprime(p=10^(k-1), 10^k-1, if (#strsplit(Str(p^n), Str(nextprime(p+1))) >= 2, return(p));); return(-1); \\ Michel Marcus, May 02 2025
Showing 1-5 of 5 results.
Comments