A068715 -id:A068715 - cp's OEIS frontend

A068712 Primes of the form 5*2^k + 3.

13, 23, 43, 83, 163, 643, 1283, 10243, 20483, 1310723, 5242883, 335544323, 1342177283, 21474836483, 85899345923, 43980465111043, 87960930222083, 5629499534213123, 22517998136852483, 1441151880758558723

Offset: 1

Amarnath Murthy, Mar 05 2002

nonn

			1283 is a term as a concatenation of 2^7 and 3.

Vincenzo Librandi, Table of n, a(n) for n = 1..38

Cf. A058586, A068715, A144487, A211486.

[a: n in [1..100] | IsPrime(a) where a is 5*2^n + 3]; // Vincenzo Librandi, Dec 08 2011

Select[5*2^Range[60]+3, PrimeQ]  (* Harvey P. Dale, Feb 04 2011 *)

for(n=1,150, if(isprime(2^n*5+3)==1,print1(2^n*5+3,",")))

More terms from Benoit Cloitre, Mar 09 2002

A354524 Primes p such that p+1 is the concatenation of a power of 3 and a power of 2.

Original entry on oeis.org

11, 13, 17, 31, 37, 97, 131, 163, 271, 277, 331, 811, 1511, 2437, 2731, 3511, 7297, 9127, 9511, 18191, 21871, 27127, 65617, 72931, 196831, 196837, 278191, 332767, 729511, 812047, 1262143, 1524287, 1968331, 2187511, 5314411, 5314417, 5904931, 6561127, 7298191, 15943237, 47829697, 53144131

Offset: 1

J. M. Bergot and Robert Israel, Aug 16 2022

			a(5) = 97 is a term because it is prime and 97 + 1 = 98 is the concatenation of 3^2 = 9 and 2^3 = 8.

Robert Israel, Table of n, a(n) for n = 1..5803

Cf. A068801. Contains A068715.

M:= 10: # for terms with <= M digits
R:= NULL:
for i from 0 while 3^i < 10^(M-1) do
  d:= 1+ilog10(3^i);
  for j from 1 while 2^j < 10^(M-d) do
    x:= dcat(3^i,2^j)-1;
    if isprime(x) then R:= R,x fi
od od:
sort([R]);

from sympy import isprime
from itertools import count, takewhile
def auptod(digits):
    M = 10**digits
    pows2 = list(takewhile(lambda x: x < M , (2**a for a in count(0))))
    pows3 = list(takewhile(lambda x: x < M , (3**b for b in count(0))))
    strs2, strs3 = list(map(str, pows2)), list(map(str, pows3))
    concat = (int(s3+s2) for s3 in strs3 for s2 in strs2)
    return sorted(set(t-1 for t in concat if t < M and isprime(t-1)))
print(auptod(10)) # Michael S. Branicky, Aug 16 2022

cp's OEIS Frontend

A068712 Primes of the form 5*2^k + 3.

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