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
Examples
8 = 2^3; 881 is prime. 27 = 3^3; 27271 is prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
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 *) -
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
Comments