A348792
Numbers k such that the reverse concatenation of the first k binary numbers A098780(k) is prime.
Original entry on oeis.org
2, 3, 4, 7, 11, 13, 25, 97, 110, 1939
Offset: 1
a(4) = 7 is because the binary number 111 110 101 100 11 10 1 (with no spaces), which is 128413 in decimal, is prime.
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q:= n-> isprime(Bits[Join](['Bits[Split](i)[]'$i=1..n])):
select(q, [$1..200])[]; # Alois P. Heinz, Dec 03 2021
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f[n_] := FromDigits[Flatten @ IntegerDigits[Range[n, 1, -1], 2], 2]; Select[Range[120], PrimeQ[f[#]] &] (* Amiram Eldar, Dec 03 2021 *)
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from sympy import isprime
def afind(limit):
s, k = "", 1
for k in range(1, limit+1):
s += bin(k)[2:][::-1]
t = int(s[::-1], 2)
if isprime(t):
print(k, end=", ")
afind(200) # Michael S. Branicky, Dec 03 2021
A300570
a(n) is the concatenation n in base 2, n-1 in base 2, ..., 1 in base 2.
Original entry on oeis.org
1, 101, 11101, 10011101, 10110011101, 11010110011101, 11111010110011101, 100011111010110011101, 1001100011111010110011101, 10101001100011111010110011101, 101110101001100011111010110011101, 1100101110101001100011111010110011101
Offset: 1
Cf.
A098780 (decimal expansion of terms).
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a:= proc(n) option remember; `if`(n=1, 1,
parse(cat(convert(n, binary), a(n-1))))
end:
seq(a(n), n=1..12); # Alois P. Heinz, Feb 19 2023
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Table[FromDigits[Flatten[IntegerDigits[#,2]&/@Range[n,1,-1]]],{n,20}] (* Harvey P. Dale, Sep 07 2020 *)
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from itertools import count, islice
def agen(): # generator of terms
s = ""
for k in count(1):
s = bin(k)[2:] + s
yield int(s)
print(list(islice(agen(), 15))) # Michael S. Branicky, Feb 19 2023
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from functools import reduce
def A300570(n): return int(bin(reduce(lambda i,j:(i<Chai Wah Wu, Feb 26 2023
A175909
Decimal representation of the binary number formed by the concatenation of digits which are the same in both the left and right binary concatenations of the integers 1 to n.
Original entry on oeis.org
1, 1, 7, 46, 29, 219, 495, 1502, 368357, 27603, 120539, 1797358, 462906349, 32361431, 33008607, 12857291758, 5972138981, 750631865, 99509722923, 13841055262, 31762354574285, 1019248986603, 8645573738319287
Offset: 1
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Module[{l,r,d},l = {}; r = {}; Table[d = IntegerDigits[x, 2]; l = Flatten[{l, d}]; r = Flatten[{d, r}]; FromDigits[ Pick[l, EvenQ[l + r]], 2], {x, 1, DESIRED_NUMBER_OF_TERMS}]]
A175910
Take the left or right binary concatenation of the numbers 1 to n, whichever is greater, delete digits identical to corresponding digits in the other concatenation, condense the remaining digits, and convert to decimal.
Original entry on oeis.org
0, 2, 2, 2, 44, 42, 178, 812, 52, 11682, 44585, 52778, 3222, 727657, 15264354, 928184, 60925872, 15976986770, 4166367305, 785545793868, 11730991244, 11804109800746, 41522369301, 3574301245885612, 198659132140236
Offset: 1
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Module[{l,r,d,ldump,larger,rdump},l = {}; r = {}; Table[d = IntegerDigits[x, 2]; l = Flatten[{l, d}]; r = Flatten[{d, r}]; If[x > 1, ldump = l; rdump = r; While[First[ldump] == First[rdump], ldump = Rest[ldump]; rdump = Rest[rdump]]; If[First[ldump] == 1, larger = ldump, larger = rdump]; FromDigits[Pick[larger, OddQ[ldump + rdump]], 2], 0], {x, 1, DESIRED_NUMBER_OF_TERMS}]]
A175913
Convert to decimal the number resulting from performing binary xnor on the corresponding digits in the left and right binary concatenations of the integers one to n.
Original entry on oeis.org
1, 4, 25, 190, 1159, 15692, 111381, 1416474, 24608235, 291074808, 5162763209, 125052555486, 2198977618351, 28389504497340, 487294161504141, 11589641752262546, 395151697837143155, 13197172619557324880
Offset: 1
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frombinrep[x_] := FromDigits[Flatten[Table[Table[If[OddQ[ n], 1, 0], {d, 1, x[[n]]}], {n, 1, Length[x]}]], 2]
repcount[x_] := Length/@Split[x]
l = {}; r = {}; Table[d = IntegerDigits[x, 2]; l = Flatten[{l, d}]; r = Flatten[{d, r}]; frombinrep[ repcount[EvenQ[l + r]]], {x, 1, DESIRED NUMBER OF TERMS HERE}]
A360508
Numbers k such that A300570(k) considered simply as a decimal string is prime.
Original entry on oeis.org
2, 4, 13, 57, 64, 349
Offset: 1
A300570(4) = 10011101 = A000040(665267) is prime, so 4 is a term.
A300570(5) = 10110011101 = 6389*1582409 is composite, so 5 is not a term.
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Select[Range[350], PrimeQ[FromDigits[Flatten[IntegerDigits[Range[#, 1, -1], 2]]]] &] (* Amiram Eldar, Feb 19 2023 *)
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from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
s = ""
for k in count(1):
s = bin(k)[2:] + s
if isprime(int(s)): yield k
print(list(islice(agen(), 5))) # Michael S. Branicky, Feb 19 2023
Showing 1-6 of 6 results.