A306265
Terms in A323711 such that deleting any existing 9 or 0 digit in decimal notation does not result in a term of A323711.
Original entry on oeis.org
142857, 285714, 15623784, 15843762, 17438256, 17562438, 18243756, 21584376, 23784156, 24375618, 24381756, 25617438, 137965842, 139657842, 157836042, 157836204, 157839642, 157840362, 157842036, 157860342, 157862034, 157963842, 158379642, 159637842, 160357842
Offset: 1
A323711(3) = 1402857. Deleting the digit 0 results in 142857 which is A323711(1). Similarly, deleting 0's and 9' from A323711(3)-A323711(20) results in another term of A323711 and a(3) = A323711(21).
A344436
Numbers k such that k, 2*k, 3*k, 4*k, 5*k and 6*k are anagrams and no digit of k is zero.
Original entry on oeis.org
142857, 1429857, 14299857, 142999857, 1429999857, 14299999857, 142857142857, 142999999857, 1428571429857, 1429857142857, 1429999999857, 14285714299857, 14298571429857, 14299857142857, 14299999999857, 137428291864557, 137464282918557, 142829186455737
Offset: 1
142857, 1429857, and 14299857 are in the sequence:
.
k 2*k 3*k 4*k 5*k 6*k
-------- -------- -------- -------- -------- --------
142857 285714 428571 571428 714285 857142
1429857 2859714 4289571 5719428 7149285 8579142
14299857 28599714 42899571 57199428 71499285 85799142
A373177
Integers k such that 2k + 1 and 4k + 3 are anagrams of k.
Original entry on oeis.org
15632, 126530, 130265, 150632, 152630, 156329, 162530, 163025, 1265030, 1265300, 1265309, 1300265, 1302650, 1302659, 1500632, 1502630, 1506329, 1526300, 1526309, 1563299, 1566332, 1625030, 1625300, 1625309, 1630025, 1630250, 1630259, 1656332, 12650030
Offset: 1
15632 is a term, since 2*15632 + 1 = 31265 and 4*15632 + 3 = 62531 are both permutations of the digits of 15632.
-
filter:= proc(n) local L;
L:= sort(convert(n,base,10));
sort(convert(2*n+1,base,10))=L
and sort(convert(4*n+3,base,10))=L
end proc:
R:= NULL: count:= 0:
for d from 1 while count < 100 do
for x from 10^(d-1) + 7 by 9 to (10^d-3)/4 while count < 100 do
if filter(x) then R:= R,x; count:= count+1 fi
od od:
R; # Robert Israel, May 27 2024
-
sid[n_] := Sort[IntegerDigits[n]]; Select[Range[13000000], sid[#] == sid[2*# + 1] == sid[4*# + 3] &] (* Amiram Eldar, May 27 2024 *)
-
isok(k) = my(d=vecsort(digits(k))); (d == vecsort(digits(2*k+1))) && (d == vecsort(digits(4*k+3))); \\ Michel Marcus, May 28 2024
-
from itertools import count, islice
def agen(): # generator of terms
for e in count(1):
for k in range(10**(e-1), 10**e//4):
if sorted(str(k)) == sorted(str(2*k+1)) == sorted(str(4*k+3)):
yield k
print(list(islice(agen(), 30))) # Michael S. Branicky, May 26 2024
Showing 1-3 of 3 results.
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