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

%I A265181 #48 Jul 23 2025 15:39:27
%S A265181 881,27271,7297291,133113311,337533751,19683196831,42875428751,
%T A265181 68921689211,1038231038231,1574641574641,2053792053791,2744274427441,
%U A265181 4218754218751,6859685968591,7290007290001,7297297297291,106120810612081,224809122480911,274400027440001,280322128032211,317652331765231,500021150002111,812060181206011,1251251251251251,1757617576175761,1968319683196831,5931959319593191
%N A265181 Prime numbers resulting from the concatenation of at least two copies of a cubic number followed by a trailing "1.".
%C A265181 Subsequence of A030430 (primes of the form 10n+1). - _Michel Marcus_, Dec 04 2015
%C A265181 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 A265181 Without the "repeated at least twice" constraint, A168147 would be a subsequence. - _Michel Marcus_, Dec 05 2015
%H A265181 Robert Israel, <a href="/A265181/b265181.txt">Table of n, a(n) for n = 1..10000</a>
%e A265181 8 = 2^3; 881 is prime.
%e A265181 27 = 3^3; 27271 is prime.
%p A265181 N:= 20: # to get all terms with at most N digits
%p A265181 M:= floor((N-1)/2):
%p A265181 res:= {}:
%p A265181 for s from 1 to floor(10^(M/3)) do
%p A265181    x:= s^3;
%p A265181    m:= 1+ilog10(x);
%p A265181    for k from 2 to floor((N-1)/m) do
%p A265181      p:= x*add(10^(1+m*i),i=0..k-1)+1;
%p A265181      if isprime(p) then res:= res union {p} fi;
%p A265181    od
%p A265181 od:
%p A265181 sort(convert(res,list)); # _Robert Israel_, Jan 13 2016
%t A265181 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 A265181 (Python)
%o A265181 from itertools import count, islice
%o A265181 from sympy import isprime
%o A265181 def A265181_gen(): # generator of terms
%o A265181     return filter(isprime,(int(str(k**3)*2)*10+1 for k in count(1)))
%o A265181 A265181_list = list(islice(A265181_gen(),20)) # _Chai Wah Wu_, Feb 20 2023
%Y A265181 Cf. A000578, A030430, A066592, A076289, A168147 , A232066.
%K A265181 nonn,base
%O A265181 1,1
%A A265181 _Thomas S. Pedigo_, Dec 03 2015