A265181 Prime numbers resulting from the concatenation of at least two copies of a cubic number followed by a trailing "1."

881, 27271, 7297291, 133113311, 337533751, 19683196831, 42875428751, 68921689211, 1038231038231, 1574641574641, 2053792053791, 2744274427441, 4218754218751, 6859685968591, 7290007290001, 7297297297291, 106120810612081, 224809122480911, 274400027440001, 280322128032211, 317652331765231, 500021150002111, 812060181206011, 1251251251251251, 1757617576175761, 1968319683196831, 5931959319593191

Offset

1,1

Comments

Subsequence of A030430 (primes of the form 10n+1). - Michel Marcus, Dec 04 2015

If m is a term then (m-1)/10 is divisible by a cube (A000578) and the resulting quotient, different from 1, is in A076289. - Michel Marcus, Dec 05 2015

Without the "repeated at least twice" constraint, A168147 would be a subsequence. - Michel Marcus, Dec 05 2015

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

8 = 2^3; 881 is prime.
27 = 3^3; 27271 is prime.

Maple

N:= 20: # to get all terms with at most N digits
M:= floor((N-1)/2):
res:= {}:
for s from 1 to floor(10^(M/3)) do
   x:= s^3;
   m:= 1+ilog10(x);
   for k from 2 to floor((N-1)/m) do
     p:= x*add(10^(1+m*i), i=0..k-1)+1;
     if isprime(p) then res:= res union {p} fi;
   od
od:
sort(convert(res, list)); # Robert Israel, Jan 13 2016

Mathematica

Take[Sort@ Flatten[Select[#, PrimeQ] & /@ Table[FromDigits@ Append[Flatten@ IntegerDigits@ Table[n^3, {#}], 1] & /@ Range[2, 20], {n, 1, 300}] /. {} -> Nothing], 27] (* Michael De Vlieger, Jan 05 2016 *)

Prog

(Python)
from itertools import count, islice
from sympy import isprime
def A265181_gen(): # generator of terms
    return filter(isprime, (int(str(k**3)*2)*10+1 for k in count(1)))
A265181_list = list(islice(A265181_gen(), 20)) # Chai Wah Wu, Feb 20 2023

Crossrefs

Cf. A000578, A030430, A066592, A076289, A168147 , A232066.

Sequence in context: A006052 A105976 A340342 * A137064 A092675 A135127

Adjacent sequences: A265178 A265179 A265180 * A265182 A265183 A265184

Keyword

nonn,base

Author

Thomas S. Pedigo, Dec 03 2015

Status

approved