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A351975
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Numbers k such that A037276(k) == -1 (mod k).
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1
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1, 6, 14, 18, 48, 124, 134, 284, 3135, 4221, 9594, 16468, 34825, 557096, 711676, 746464, 1333334, 2676977, 6514063, 11280468, 16081252, 35401658, 53879547, 133333334, 198485452, 223856659, 1333333334, 2514095219, 2956260256, 3100811124, 10912946218, 19780160858
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Numbers k such that the concatenation of prime factors of k is 1 less than a multiple of k.
Terms k where k-1 is prime include 6, 14, 18, 48 and 284. Are there others?
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LINKS
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EXAMPLE
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a(4) = 48 is a term because 48=2*2*2*2*3 and 22223 == -1 (mod 48).
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MAPLE
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tcat:= proc(x, y) x*10^(1+ilog10(y))+y end proc:
filter:= proc(n) local F, t, i;
F:= map(t -> t[1]$t[2], sort(ifactors(n)[2], (a, b)->a[1]<b[1]));
t:= F[1];
for i from 2 to nops(F) do
t:= tcat(t, F[i])
od;
t mod n = n-1
end proc:
filter(1):= true:
select(filter, [$1..10^8]);
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PROG
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(Python)
from sympy import factorint
if n == 1: return 1
return int("".join(str(p)*e for p, e in sorted(factorint(n).items())))
def afind(limit, startk=1):
for k in range(startk, limit+1):
print(k, end=", ")
(Python)
from itertools import count, islice
from sympy import factorint
def A351975_gen(startvalue=1): # generator of terms >= startvalue
for k in count(max(startvalue, 1)):
c = 0
for d in sorted(factorint(k, multiple=True)):
c = (c*10**len(str(d)) + d) % k
if c == k-1:
yield k
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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