cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A066593 Primes which can be expressed as concatenation of powers of 2 and 0's.

Original entry on oeis.org

2, 11, 41, 101, 181, 211, 241, 281, 401, 421, 641, 811, 821, 881, 1021, 1181, 1201, 1321, 1481, 1601, 1621, 1801, 1811, 2011, 2081, 2111, 2141, 2161, 2221, 2281, 2411, 2441, 2801, 3221, 4001, 4021, 4111, 4201, 4211, 4241, 4421, 4441, 4481
Offset: 1

Views

Author

Amarnath Murthy, Dec 21 2001

Keywords

Examples

			1321 is a term as it is a concatenation of 1, 32 and 1 which are powers of 2.

Crossrefs

Cf. A066591, A066592.

Extensions

Corrected and extended by Christopher Lund (clund(AT)san.rr.com), Apr 14 2002

A173580 Primes where each digit is 0, 1, 2, 4, or 8.

Original entry on oeis.org

2, 11, 41, 101, 181, 211, 241, 281, 401, 421, 811, 821, 881, 1021, 1181, 1201, 1481, 1801, 1811, 2011, 2081, 2111, 2141, 2221, 2281, 2411, 2441, 2801, 4001, 4021, 4111, 4201, 4211, 4241, 4421, 4441, 4481, 4801, 8011, 8081, 8101, 8111, 8221, 8821, 10111
Offset: 1

Views

Author

Michel Lagneau, Feb 22 2010

Keywords

Links

Crossrefs

See A066593.
Cf. A066591, A066592.

Programs

  • Maple
    with(numtheory): for n from 2 to 10000 do: l:=evalf(floor(ilog10(n))+1): n0:=n:indic:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10): n0:=v : if u=3 or u= 5 or u= 6 or u=7 or u=9 then indic :=1 :else fi :od :if indic = 0 and type(n,prime) = true then print(n):else fi:od:
  • Mathematica
    Join[{2}, Select[Map[FromDigits, Tuples[{0, 1, 2, 4, 8}, 3]]*10 + 1, PrimeQ]] (* Paolo Xausa, Jun 12 2025 *)
  • Python
    from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    yield 2
    yield from (t for digits in count(2) for f in "1248" for mid in product("01248", repeat=digits-2) if isprime(t:=int(f + "".join(mid) + "1")))
print(list(islice(agen(), 45))) # Michael S. Branicky, Jun 11 2025

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

Original entry on oeis.org

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

Views

Author

Thomas S. Pedigo, Dec 03 2015

Keywords

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

Examples

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

Links

Crossrefs

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

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

A066594 Primes which can be expressed as concatenation of powers of 3 and 0's.

Original entry on oeis.org

3, 11, 13, 19, 31, 101, 103, 109, 113, 127, 131, 139, 181, 191, 193, 199, 271, 311, 313, 331, 811, 911, 919, 991, 1009, 1013, 1019, 1031, 1033, 1039, 1091, 1093, 1103, 1109, 1181, 1193, 1279, 1301, 1303, 1319, 1327, 1381, 1399, 1811, 1901, 1913, 1931
Offset: 1

Views

Author

Amarnath Murthy, Dec 21 2001

Keywords

Examples

			271 is a term as it is a concatenation of 27 and 1 which are powers of 3.

Crossrefs

Cf. A066591, A066592, A066593.

Extensions

Corrected and extended by Christopher Lund (clund(AT)san.rr.com), Apr 14 2002
Showing 1-4 of 4 results.

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