A354524 - OEIS

%I #15 Aug 18 2022 11:45:16

%S 11,13,17,31,37,97,131,163,271,277,331,811,1511,2437,2731,3511,7297,

%T 9127,9511,18191,21871,27127,65617,72931,196831,196837,278191,332767,

%U 729511,812047,1262143,1524287,1968331,2187511,5314411,5314417,5904931,6561127,7298191,15943237,47829697,53144131

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

%H Robert Israel, <a href="/A354524/b354524.txt">Table of n, a(n) for n = 1..5803</a>

%e 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.

%p M:= 10: # for terms with <= M digits

%p R:= NULL:

%p for i from 0 while 3^i < 10^(M-1) do

%p   d:= 1+ilog10(3^i);

%p   for j from 1 while 2^j < 10^(M-d) do

%p     x:= dcat(3^i,2^j)-1;

%p     if isprime(x) then R:= R,x fi

%p od od:

%p sort([R]);

%o (Python)

%o from sympy import isprime

%o from itertools import count, takewhile

%o def auptod(digits):

%o     M = 10**digits

%o     pows2 = list(takewhile(lambda x: x < M , (2**a for a in count(0))))

%o     pows3 = list(takewhile(lambda x: x < M , (3**b for b in count(0))))

%o     strs2, strs3 = list(map(str, pows2)), list(map(str, pows3))

%o     concat = (int(s3+s2) for s3 in strs3 for s2 in strs2)

%o     return sorted(set(t-1 for t in concat if t < M and isprime(t-1)))

%o print(auptod(10)) # _Michael S. Branicky_, Aug 16 2022

%Y Cf. A068801. Contains A068715.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Aug 16 2022