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A354524
Primes p such that p+1 is the concatenation of a power of 3 and a power of 2.
1
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
1,1
LINKS
EXAMPLE
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.
MAPLE
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]);
PROG
(Python)
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
CROSSREFS
Cf. A068801. Contains A068715.
Sequence in context: A266675 A185104 A240570 * A162237 A325870 A090236
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Aug 16 2022
STATUS
approved