%I #46 Feb 20 2023 14:50:05

%S 881,27271,7297291,133113311,337533751,19683196831,42875428751,

%T 68921689211,1038231038231,1574641574641,2053792053791,2744274427441,

%U 4218754218751,6859685968591,7290007290001,7297297297291,106120810612081,224809122480911,274400027440001,280322128032211,317652331765231,500021150002111,812060181206011,1251251251251251,1757617576175761,1968319683196831,5931959319593191

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

%C Subsequence of A030430 (primes of the form 10n+1). - _Michel Marcus_, Dec 04 2015

%C 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

%C Without the "repeated at least twice" constraint, A168147 would be a subsequence. - _Michel Marcus_, Dec 05 2015

%H Robert Israel, <a href="/A265181/b265181.txt">Table of n, a(n) for n = 1..10000</a>

%e 8 = 2^3; 881 is prime.

%e 27 = 3^3; 27271 is prime.

%p N:= 20: # to get all terms with at most N digits

%p M:= floor((N-1)/2):

%p res:= {}:

%p for s from 1 to floor(10^(M/3)) do

%p x:= s^3;

%p m:= 1+ilog10(x);

%p for k from 2 to floor((N-1)/m) do

%p p:= x*add(10^(1+m*i),i=0..k-1)+1;

%p if isprime(p) then res:= res union {p} fi;

%p od

%p od:

%p sort(convert(res,list)); # _Robert Israel_, Jan 13 2016

%t 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 *)

%o (Python)

%o from itertools import count, islice

%o from sympy import isprime

%o def A265181_gen(): # generator of terms

%o return filter(isprime,(int(str(k**3)*2)*10+1 for k in count(1)))

%o A265181_list = list(islice(A265181_gen(),20)) # _Chai Wah Wu_, Feb 20 2023

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

%K nonn,base

%O 1,1

%A _Thomas S. Pedigo_, Dec 03 2015