A038447 -id:A038447 - cp's OEIS frontend

A038451 Sums of 9 distinct powers of 10.

111111111, 1011111111, 1101111111, 1110111111, 1111011111, 1111101111, 1111110111, 1111111011, 1111111101, 1111111110, 10011111111, 10101111111, 10110111111, 10111011111, 10111101111, 10111110111, 10111111011

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038452, A038453, A038454.

Sort[Plus @@@ Subsets[10^Range[0, 10], {9}]] (* Amiram Eldar, Jul 12 2022 *)

from itertools import islice
def A038451_gen(): # generator of terms
    yield int(bin(n:=511)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038451_list = list(islice(A038451_gen(),20)) # Chai Wah Wu, Mar 11 2025

Offset corrected by Amiram Eldar, Jul 12 2022

A038467 Sums of 5 distinct powers of 3.

Original entry on oeis.org

121, 283, 337, 355, 361, 363, 769, 823, 841, 847, 849, 985, 1003, 1009, 1011, 1057, 1063, 1065, 1081, 1083, 1089, 2227, 2281, 2299, 2305, 2307, 2443, 2461, 2467, 2469, 2515, 2521, 2523, 2539, 2541, 2547, 2929, 2947, 2953, 2955, 3001, 3007, 3009, 3025, 3027, 3033

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Base 3 interpretation of A038447.

Cf. A000244, A038464, A038465, A038466, A038468, A038469.

Union[Total/@Subsets[3^Range[0,7],{5}]]  (* Harvey P. Dale, Feb 23 2011 *)

A038473 Sums of 5 distinct powers of 4.

Original entry on oeis.org

341, 1109, 1301, 1349, 1361, 1364, 4181, 4373, 4421, 4433, 4436, 5141, 5189, 5201, 5204, 5381, 5393, 5396, 5441, 5444, 5456, 16469, 16661, 16709, 16721, 16724, 17429, 17477, 17489, 17492, 17669, 17681, 17684, 17729, 17732, 17744, 20501, 20549, 20561, 20564, 20741

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Base 4 interpretation of A038447.

Cf. A000302, A038470, A038471, A038472.

Take[Total/@Subsets[4^Range[0,10],{5}]//Union,50] (* Harvey P. Dale, Oct 02 2016 *)

from itertools import islice
def A038473_gen(): # generator of terms
    yield int(bin(n:=31)[2:],4)
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:],4)
A038473_list = list(islice(A038473_gen(),30)) # Chai Wah Wu, Apr 04 2025

A038477 Sums of 5 distinct powers of 5.

Original entry on oeis.org

781, 3281, 3781, 3881, 3901, 3905, 15781, 16281, 16381, 16401, 16405, 18781, 18881, 18901, 18905, 19381, 19401, 19405, 19501, 19505, 19525, 78281, 78781, 78881, 78901, 78905, 81281, 81381, 81401, 81405, 81881, 81901, 81905, 82001, 82005, 82025, 93781, 93881, 93901

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Base 5 interpretation of A038447.

Cf. A000351, A038474, A038475, A038476.

Union[Total[5^#]&/@Subsets[Range[0,8],{5}]] (* Harvey P. Dale, Nov 15 2012 *)

from itertools import islice
def A038477_gen(): # generator of terms
    yield int(bin(n:=31)[2:],5)
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:],5)
A038477_list = list(islice(A038477_gen(),30)) # Chai Wah Wu, Apr 05 2025

Offset corrected by Amiram Eldar, Jul 13 2022

A383918 Primes made up of 0's and five 1's only.

Original entry on oeis.org

101111, 10011101, 10101101, 10110011, 10111001, 11000111, 11100101, 100100111, 100111001, 101001011, 101100011, 110010101, 110101001, 111000101, 111001001, 1000011011, 1000110101, 1001000111, 1001001011, 1001010011, 1010000111, 1010001101, 1010010011, 1010100011, 1010110001

Offset: 1

René-Louis Clerc, May 15 2025

Expression of the primes that are 0-successors of the preprime 11111 (= 41*271); they constitute the infinite set of secondary primes with five 1's and zeros denoted {11111} (Definitions 1, 2, 3, 4 of Clerc).

Robert Israel, Table of n, a(n) for n = 1..10000
René-Louis Clerc, Nombres premiers primaires et nombres premiers secondaires, 2025.

Cf. A157711, A038447, A020449.

f:= proc(n) local R,c,i;
 sort(select(isprime, [seq(1+10^(n-1) + add(10^i,i=c), c=combinat:-choose(n-2,3))]))
end proc:
map(op,[seq(f(i),i=6..10)]); # Robert Israel, May 29 2025

list(M) = for(i=3, M, for(j=2, i-1, for(k=1, j-1, for(r=1, k-1, my(p=10^i+10^j+10^k+10^r+1); isprime(p) && print1(p, ", ")))))

from itertools import count, islice
from sympy import isprime
def A383918_gen(): # generator of terms
    for a in count(4):
        for b in range(3,a):
            for c in range(2,b):
                for d in range(1,c):
                    if isprime(p:=10**a+10**b+10**c+10**d|1):
                        yield(p)
A383918_list = list(islice(A383918_gen(),30)) # Chai Wah Wu, May 29 2025

A383919 Primes made up of 0's and seven 1's only.

Original entry on oeis.org

11110111, 11111101, 101101111, 101111011, 110111011, 111010111, 1001110111, 1010011111, 1011110011, 1100101111, 1101010111, 1101110011, 1110011101, 1110110011, 1111100101, 1111110001, 10010110111, 10011101011, 10011110101, 10100111101, 10111001011, 10111110001, 11001011101

Offset: 1

René-Louis Clerc, May 15 2025

Expression of the primes that are 0-successors of the preprime 1111111 (= 239*4649); they constitute the infinite set of secondary primes with seven 1's and zeros denoted {1111111} (Definitions 1, 2, 3, 4 of Clerc).

Alois P. Heinz, Table of n, a(n) for n = 1..12277
René-Louis Clerc, Nombres premiers primaires et nombres premiers secondaires, 2025.

Intersection of A020449 and A062337.

Cf. A157711, A038447, A020449.

list(M) = for(i=3, M, for(j=2, i-1, for(k=1, j-1, for(r=1, k-1, for(l=1, r-1, for(m=1, l-1, my(p=10^i+10^j+10^k+10^r+10^l+10^m+1); isprime(p) && print1(p, ", ")))))))

from itertools import count, islice
from sympy import isprime
def A383919_gen(): # generator of terms
    for a in count(6):
        for b in range(5,a):
            for c in range(4,b):
                for d in range(3,c):
                    for e in range(2,d):
                        for f in range(1,e):
                            if isprime(p:=10**a+10**b+10**c+10**d+10**e+10**f|1):
                                yield(p)
A383919_list = list(islice(A383919_gen(),23)) # Chai Wah Wu, May 28 2025

cp's OEIS Frontend

A038451 Sums of 9 distinct powers of 10.

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A038467 Sums of 5 distinct powers of 3.

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A038473 Sums of 5 distinct powers of 4.

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A038477 Sums of 5 distinct powers of 5.

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A383918 Primes made up of 0's and five 1's only.

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A383919 Primes made up of 0's and seven 1's only.

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