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

1,1

Links

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

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

Adjacent sequences: A354521 A354522 A354523 * A354525 A354526 A354527

Keyword

nonn,base

Author

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

Status

approved