A082705 -id:A082705 - cp's OEIS frontend

A056252 Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) - 7 for n > 0.

5, 7, 893, 1523, 3035, 21155

Offset: 1

Robert G. Wilson v, Aug 18 2000

Numbers n such that (290*10^n + 7)/9 is prime.
Numbers n such that the digit 3 followed by n >= 0 occurrences of the digit 2 followed by the digit 3 is prime.
Numbers corresponding to terms <= 3035 are certified primes.

			3222223 is prime, hence 5 is a term.

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Patrick De Geest, PDP Reference Table - 323.
Makoto Kamada, Prime numbers of the form 322...223.
Index entries for primes involving repunits.

Cf. A000533, A002275, A082705.

Select[Range[0, 2000], PrimeQ[(290 10^# + 7) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

a=33;for(n=0,1600,if(isprime(a),print1(n,","));a=10*a-7)

for(n=0,1600,if(isprime((290*10^n+7)/9),print1(n,",")))

a(n) = A082705(n) - 2.

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004
Edited by N. J. A. Sloane, Apr 17 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Comments section updated and a link added by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 05 2014

A375261 Smallest n-digit reversible prime with only prime digits.

Original entry on oeis.org

2, 37, 337, 3257, 32233, 322573, 3222223, 32235223, 322222223, 3222222257, 32222232577, 322222232537, 3222222223333, 32222222332733, 322222222237537, 3222222222223373, 32222222222223353, 322222222222225333, 3222222222222222577, 32222222222222225573, 322222222222222233253

Offset: 1

Jean-Marc Rebert, Aug 08 2024

Differs from A177513(n) for n in A082705. - Robert Israel, May 11 2025

Robert Israel, Table of n, a(n) for n = 1..243

Cf. A006567, A082705, A160748, A177513.

PD:= [2,3,5,7]:
g:= proc(n) local L,d,i,x,y;
  L:= convert(n,base,4); d:= nops(L);
  x:= add(PD[L[i]+1]*10^(i-1),i=1..d);
  y:= add(PD[L[-i]+1]*10^(i-1),i=1..d);
  if isprime(x) and isprime(y) then return x fi;
end proc:
f:= proc(d) local k,v;
  for k from 4^(d-1) do v:= g(k); if v <> NULL then return v fi od
end proc;
f(1):= 2:
map(f, [$1..30]); # Robert Israel, May 11 2025

from sympy import isprime
from itertools import product
def a(n):
    if n == 1: return 2
    for first in "37":
        for rest in product("2357", repeat=n-1):
            s = first + "".join(rest)
            if isprime(t:=int(s)) and isprime(int(s[::-1])):
                return t
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Aug 08 2024

a(n) <= A177513(n) for n > 1.

If a(n) is not a palindrome, a(n) = A177513(n) for n > 1.

cp's OEIS Frontend

A056252 Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) - 7 for n > 0.

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