A069662
Largest n-digit prime with maximum digit sum.
Original entry on oeis.org
7, 89, 997, 8999, 99989, 989999, 9899999, 99999989, 998999999, 9999898999, 99989999999, 999999999989, 9999999999799, 99999999899999, 999999999999989, 9999999999989999, 99999999999899999, 999999999999999989, 9998999999999999999, 99999999999999999989
Offset: 1
More terms from
Rick L. Shepherd, Jul 15 2002. a(5) through a(20) have been certified prime with Primo.
A069663
Smallest n-digit prime with minimum digit sum.
Original entry on oeis.org
2, 11, 101, 1021, 10111, 100003, 1000003, 10010101, 101001001, 1000000021, 10000001101, 100000000003, 1000000020001, 10000000001011, 100000000100101, 1000000000100011, 10000000000001101, 100000000000000003
Offset: 1
a(5) = 10111 is the least prime with digit sum 4 and no other/smaller 5 digit prime has a digit sum 4 or less.
A069664
Largest n-digit prime with minimum digit sum.
Original entry on oeis.org
2, 11, 101, 3001, 21001, 102001, 2100001, 30000001, 200001001, 2010000001, 30000000001, 110000000101, 2000001000001, 20000000100001, 200000010000001, 1100010000000001, 20000001000000001, 110000000000000101, 2000000000000100001, 20000000100000000001
Offset: 1
-
Table[ Max[ Flatten[Table[ If[PrimeQ[10^n + 1], 10^n + 1, If[PrimeQ[10^n + 10^i + 10^j + 1], 10^n + 10^i + 10^j + 1, 0]], {i, 0, n}, {j, 0, i}]]], {n, 0, 50}] (* Program works so long as there exists an n-digit prime with digit sum 4 or less. *)
A241206
Greatest n-digit prime having at least n-1 identical digits.
Original entry on oeis.org
7, 97, 997, 9949, 99991, 999979, 9999991, 99999989, 999999929, 9999999929, 99999999599, 999999999989, 9999999999799, 99999999999959, 999999999999989, 9999999999999199, 99999999999999997, 999999999999999989, 9999999999999999919, 99999999999999999989, 999999999999999999899, 9999999999999999999929
Offset: 1
-
with(numtheory):lst:={}:nn:=30:kk:=0:T:=array(1..nn):U:=array(1..20):
for n from 2 to nn do:
for i from 1 to n do:
T[i]:=9:
od:
ii:=0:
for j from 1 to n while(ii=0)do:
for k from 9 by -1 to 0 while(ii=0)do:
T[n-j+1]:=k:s:=sum('T[i]*10^(n-i)', 'i'=1..n):
if type(s,prime)=true and length(s)=n
then
ii:=1: kk:=kk+1:U[kk]:=s:
else
T[n-j+1]:=9:
fi:
od:
od:
od :
print(U) :
-
Table[SelectFirst[Reverse@ Prime@ Range[PrimePi[10^(n - 1)] + 1, PrimePi[10^n - 1]], Max@ DigitCount@ # >= (n - 1) &], {n, 2, 8}]
(* WARNING: the following assumes the conjecture is true WARNING *)
Table[SelectFirst[Select[Reverse@ Union@ Map[FromDigits, Join @@ Map[Permutations[Append[Table[9, {n - 1}], #]] &, Range[0, 9]]], PrimeQ@ # && IntegerLength@ # == n &], Max@ DigitCount@ # >= (n - 1) &], {n, 2, 20}] (* Michael De Vlieger, Dec 10 2015, Version 10 *)
-
from _future_ import division
from sympy import isprime
def A241206(n):
for i in range(9,0,-1):
x = i*(10**n-1)//9
for j in range(n-1,-1,-1):
for k in range(9-i,-1,-1):
y = x + k*(10**j)
if isprime(y):
return y
for j in range(n):
for k in range(1,i+1):
if j < n-1 or k < i:
y = x-k*(10**j)
if isprime(y):
return y # Chai Wah Wu, Dec 29 2015
A069665
Smallest n-digit square with maximum digit sum.
Original entry on oeis.org
9, 49, 289, 6889, 97969, 698896, 9696996, 79869969, 876988996, 8998988769, 88998998929, 975979998889, 9998768898889, 97888999968769, 898999897988929, 9895699989899689, 38999699989995889, 989879999979599689
Offset: 1
More terms from Larry Reeves (larryr(AT)acm.org), Oct 14 2003
A069666
Largest n-digit square with maximum digit sum.
Original entry on oeis.org
9, 49, 784, 6889, 97969, 877969, 9696996, 88679889, 876988996, 8998988769, 88998998929, 975979998889, 9998768898889, 97888999968769, 898999897988929, 9896999999766889, 99497897999899876, 989879999979599689
Offset: 1
Corrected and extended by Larry Reeves (larryr(AT)acm.org), Oct 14 2003
A069667
Smallest nontrivial (no trailing zeros) n-digit square with minimum digit sum.
Original entry on oeis.org
1, 16, 121, 1024, 10201, 101124, 1002001, 24000201, 100020001, 2500100001, 10000200001, 141001001001, 1000002000001, 25000010000001, 100000020000001, 2500000100000001, 10000000200000001, 250000001000000001
Offset: 1
More terms from Larry Reeves (larryr(AT)acm.org), Oct 15 2003
A069668
Largest nontrivial (no trailing zeros) n-digit square with minimum digit sum.
Original entry on oeis.org
1, 25, 121, 2401, 10201, 301401, 1002001, 25010001, 100020001, 2500100001, 10000200001, 250001000001, 1000002000001, 25000010000001, 100000020000001, 2500000100000001, 10000000200000001, 250000001000000001
Offset: 1
Corrected and extended by Larry Reeves (larryr(AT)acm.org), Oct 15 2003
A069669
Smallest n-digit triangular number with maximum digit sum.
Original entry on oeis.org
6, 78, 496, 8778, 58996, 887778, 5897895, 88877778, 686999778, 9876799878, 89996788896, 777887999778, 7798988788878, 77779987999896, 589598998999878, 7898898998885986, 78999997699698778, 999699998689998991
Offset: 1
More terms from Larry Reeves (larryr(AT)acm.org), Oct 15 2003
A069670
Largest n-digit triangular number with maximum digit sum.
Original entry on oeis.org
6, 78, 946, 8778, 58996, 998991, 9979278, 98989485, 886899786, 9998888991, 89996788896, 999998497578, 9869988988965, 99989985868878, 988895779999896, 9999678588989986, 99889886986899778, 999699998689998991
Offset: 1
More terms from Larry Reeves (larryr(AT)acm.org), Oct 15 2003
Showing 1-10 of 14 results.
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