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Search: a020467 -id:a020467
Displaying 1-8 of 8 results found. page 1
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A260827 Primes that contain only the digits (0, 5, 7). +10
6
5, 7, 557, 577, 757, 5077, 5507, 5557, 7057, 7507, 7577, 7757, 50077, 50707, 50777, 55057, 57077, 57557, 70507, 75557, 75577, 75707, 77557, 500057, 500777, 505777, 507077, 507557, 507757, 550007, 550577, 550757, 555077, 555557, 555707, 557057, 570077, 575077 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
MATHEMATICA
Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {0, 5, 7}]=={} &]
PROG
(Magma) [p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0, 5, 7]];
(Python)
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
n, digits, alst = 0, 1, []
while len(alst) < terms:
mpstr = "".join(d*digits for d in "057")
for mp in multiset_permutations(mpstr, digits):
if mp[0] == "0": continue
t = int("".join(mp))
if isprime(t): alst.append(t)
if len(alst) == terms: break
else: digits += 1
return alst
print(aupton(38)) # Michael S. Branicky, May 07 2021
CROSSREFS
A020467 is a subsequence.
Cf. Primes that contain only the digits (k,5,7): this sequence (k=0), A260828 (k=1), A214705 (k=2), A087363 (k=3), A217039 (k=4), A260829 (k=6), A260830 (k=8), A260831 (k=9).
Cf. A000040.
KEYWORD
nonn,easy,base
AUTHOR
Vincenzo Librandi, Aug 01 2015
STATUS
approved
A284380 Numbers n with digits 5 and 7 only. +10
6
5, 7, 55, 57, 75, 77, 555, 557, 575, 577, 755, 757, 775, 777, 5555, 5557, 5575, 5577, 5755, 5757, 5775, 5777, 7555, 7557, 7575, 7577, 7755, 7757, 7775, 7777, 55555, 55557, 55575, 55577, 55755, 55757, 55775, 55777, 57555, 57557, 57575, 57577, 57755, 57757 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000
MATHEMATICA
Join @@ ((FromDigits /@ Tuples[{5, 7}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)
PROG
(Magma) [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 7}]
(Python)
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
n, digits, alst = 0, 1, []
while len(alst) < terms:
mpstr = "".join(d*digits for d in "57")
for mp in multiset_permutations(mpstr, digits):
alst.append(int("".join(mp)))
if len(alst) == terms: break
else: digits += 1
return alst
print(aupton(44)) # Michael S. Branicky, May 07 2021
CROSSREFS
Prime terms are in A020467.
Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), this sequence (k = 7), A284381 (k = 8), A284382 (k = 9).
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, Mar 28 2017
STATUS
approved
A260831 Primes that contain only the digits (5, 7, 9). +10
4
5, 7, 59, 79, 97, 557, 577, 599, 757, 797, 977, 997, 5557, 5779, 7559, 7577, 7757, 7759, 55579, 55799, 55997, 57557, 57559, 57977, 59557, 59779, 59797, 59957, 59999, 75557, 75577, 75797, 75979, 75997, 77557, 77797, 77977, 77999, 79559, 79579, 79757, 79777 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A020467, A020468 and A020471 are subsequences.
Subsequence of A030096.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
MATHEMATICA
Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 7, 9}] == {} &]
PROG
(Magma) [p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [5, 7, 9]];
CROSSREFS
Cf. similar sequences listed in A260827.
Cf. A000040, A020467, A020468, A020471, A030096.
KEYWORD
nonn,easy,base
AUTHOR
Vincenzo Librandi, Aug 03 2015
STATUS
approved
A260828 Primes that contain only the digits (1, 5, 7). +10
3
5, 7, 11, 17, 71, 151, 157, 557, 571, 577, 751, 757, 1117, 1151, 1171, 1511, 1571, 1777, 5171, 5557, 5711, 5717, 7151, 7177, 7517, 7577, 7717, 7757, 11117, 11171, 11177, 11551, 11717, 11777, 15511, 15551, 17117, 17551, 51151, 51157, 51511, 51517, 51551, 51577 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
MATHEMATICA
Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 5, 7}] == {} &]
PROG
(Magma) [p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1, 5, 7]];
(Python)
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
n, digits, alst = 0, 1, []
while len(alst) < terms:
mpstr = "".join(d*digits for d in "157")
for mp in multiset_permutations(mpstr, digits):
t = int("".join(mp))
if isprime(t): alst.append(t)
if len(alst) == terms: break
else: digits += 1
return alst
print(aupton(44)) # Michael S. Branicky, May 07 2021
CROSSREFS
A020453, A020455 and A020467 are subsequences.
Subsequence of A030096.
Cf. similar sequences listed in A260827.
Cf. A000040.
KEYWORD
nonn,easy,base
AUTHOR
Vincenzo Librandi, Aug 02 2015
STATUS
approved
A036320 Composite numbers whose prime factors contain no digits other than 5 and 7. +10
2
25, 35, 49, 125, 175, 245, 343, 625, 875, 1225, 1715, 2401, 2785, 2885, 3125, 3785, 3899, 4039, 4375, 5299, 6125, 8575, 12005, 13925, 14425, 15625, 16807, 18925, 19495, 20195, 21875, 26495, 27293, 27785, 28273, 30625, 37093, 37885, 38785 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are a product of at least two terms of A020467. - David A. Corneth, Oct 09 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for sequences related to prime factors.
FORMULA
Sum_{n>=1} 1/a(n) = Product_{p in A020467} (p/(p - 1)) - Sum_{p in A020467} 1/p - 1 = 0.1179595738... . - Amiram Eldar, May 22 2022
CROSSREFS
Cf. A003595, A020467, A036302-A036325.
KEYWORD
nonn,easy,base
AUTHOR
Patrick De Geest, Dec 15 1998
STATUS
approved
A260829 Primes that contain only the digits (5, 6, 7). +10
2
5, 7, 67, 557, 577, 677, 757, 5557, 5657, 6577, 7577, 7757, 55667, 56767, 57557, 57667, 65557, 65657, 65677, 65777, 67567, 67577, 67757, 67777, 75557, 75577, 75767, 76667, 76757, 76777, 77557, 555557, 555677, 555767, 557567, 565567, 565667, 566557, 566567 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A020467 and A020469 are subsequences.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
MATHEMATICA
Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 6, 7}] == {} &]
PROG
(Magma) [p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [5, 6, 7]];
CROSSREFS
Cf. similar sequences listed in A260827.
Cf. A020467, A020469.
KEYWORD
nonn,easy,base
AUTHOR
Vincenzo Librandi, Aug 02 2015
STATUS
approved
A260830 Primes that contain only the digits (5, 7, 8). +10
2
5, 7, 557, 577, 587, 757, 787, 857, 877, 887, 5557, 5857, 7577, 7757, 7877, 8887, 55787, 57557, 57587, 57787, 58757, 58787, 75557, 75577, 75787, 77557, 77587, 78577, 78787, 78857, 78877, 78887, 85577, 87557, 87587, 87877, 87887, 555557, 555857, 557857, 558587 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A020467 and A020470 are subsequences.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
MATHEMATICA
Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 7, 8}] == {} &]
Select[Flatten[Table[FromDigits/@Tuples[{5, 7, 8}, n], {n, 6}]], PrimeQ] (* Harvey P. Dale, Oct 06 2017 *)
PROG
(Magma) [p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [5, 7, 8]];
CROSSREFS
Cf. similar sequences listed in A260827.
Cf. A020467, A020470.
KEYWORD
nonn,easy,base
AUTHOR
Vincenzo Librandi, Aug 02 2015
STATUS
approved
A036946 Smallest n-digit prime containing only the digits 5 and 7, or 0 if no such prime exists. +10
1
5, 0, 557, 5557, 57557, 555557, 5555777, 55555777, 555557557, 5555555557, 55555555777, 555555575557, 5555555757757, 55555555575757, 555555555555557, 5555555555557577, 55555555555777777, 555555555557557757, 5555555555555557577, 55555555555575755777 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Jinyuan Wang, Table of n, a(n) for n = 1..500
MATHEMATICA
Flatten[Join[{5, 0}, Table[Select[FromDigits/@(Join[#, {7}]&/@Tuples[ {5, 7}, n]), PrimeQ, 1], {n, 2, 20}]]] (* Harvey P. Dale, Mar 08 2013 *)
CROSSREFS
Cf. A020467, A036229, A036320.
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Jan 04 1999
EXTENSIONS
More terms from Harvey P. Dale, Mar 08 2013
STATUS
approved
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Last modified August 30 00:57 EDT 2024. Contains 375520 sequences. (Running on oeis4.)