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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." 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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A006052 A105976 A340342 * A137064 A092675 A135127
KEYWORD
nonn,base
AUTHOR
Thomas S. Pedigo, Dec 03 2015
STATUS
approved

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Last modified July 13 23:31 EDT 2024. Contains 374290 sequences. (Running on oeis4.)