A354524 Primes p such that p+1 is the concatenation of a power of 3 and a power of 2.
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
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..5803
Programs
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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]); -
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