OFFSET
1,1
COMMENTS
The pairs of the form (2^k+1, 2^k) are members => the sequence is infinite.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..2000
EXAMPLE
The pair (20, 9) is in the sequence because D(20) = {2, 5}, D(9) = {3} => D(20 + 9 + 1) = D(30) = {2, 3, 5} = D(20) union D(9).
MAPLE
with(numtheory):nn:=150:
for a from 3 to nn do:
x:=factorset(a):n0:=nops(x):A:={op(x), x[n0]}:
for b from 2 to a-1 do:
y:=factorset(b):n1:=nops(y):B:={op(y), y[n1]}:
z:=factorset(a+b+1):n2:=nops(z):C:={op(z), z[n2]}:
if C = A union B
then
printf(`%d, `, a):printf(`%d, `, b):else
fi:
od:
od:
MATHEMATICA
d[n_] := First /@ FactorInteger[n]; Flatten@ Reap[ Do[ dx = d[x]; Do[ If[ d[x + y + 1] == Union[dx, d[y]], Sow[{x, y}]], {y, x-1}], {x, 2, 144}]][[2, 1]] (* Giovanni Resta, Mar 23 2017 *)
PROG
(Python)
from sympy.ntheory import primefactors
l=[]
for x in range(2, 145):
for y in range(2, x):
if primefactors(x + y + 1) == sorted(primefactors(x) + primefactors(y)):
l+=[x, y]
print(l) # Indranil Ghosh, Mar 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 21 2017
STATUS
approved