A263431
Near-repdigit primes with only digits 9 and a single 8 in decimal expansion.
Original entry on oeis.org
89, 8999, 98999, 99989, 989999, 9899999, 89999999, 99899999, 99998999, 99999989, 998999999, 98999999999, 99989999999, 999998999999, 999999999899, 999999999989, 99899999999999, 99999899999999, 99999999899999, 999999899999999, 999999999989999, 999999999999989
Offset: 1
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Select[Flatten[Table[FromDigits/@Permutations[PadRight[{8},n,9]],{n,15}]],PrimeQ] (* Harvey P. Dale, Mar 29 2020 *)
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a002283(n) = 10^n-1
a011557(n) = 10^n
num(n, k) = a002283(n)-a011557(k)
terms(n) = i=0; x=1; while(x > 0, y=x-1; while(y >= 0, if(ispseudoprime(num(x, y)), print1(num(x, y), ", "); i++); if(i==n, break({2})); y--); x++)
terms(30) \\ print initial thirty terms
A069671
Smallest n-digit triangular number with minimum digit sum.
Original entry on oeis.org
1, 10, 120, 2211, 10011, 112101, 2001000, 10006101, 200010000, 1210000221, 20000100000, 210010000005, 2000001000000, 32000004000000, 200000010000000, 3200000040000000, 20000000100000000, 320000000400000000, 2000000001000000000, 32000000004000000000
Offset: 1
A215559
Smallest n-digit noncomposite number (written in base 2) with maximum base-2 digit sum.
Original entry on oeis.org
1, 11, 111, 1011, 11111, 101111, 1111111, 10111111, 101111111, 1111011111, 11111110111, 110111111111, 1111111111111, 11101111111111, 100111111111111, 1111011111111111, 11111111111111111, 111011111111111111, 1111111111111111111, 10111111111111111111
Offset: 1
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A215559 := proc(n)
local ds,a,k;
ds := 0 ;
a := 0 ;
for k from 2^(n-1) to 2^n-1 do
if isprime(k) or k = 1 then
if A000120(k) > ds then
ds := A000120(k) ;
a := A007088(k) ;
end if;
end if;
end do:
a ;
end proc: # R. J. Mathar, Aug 23 2012
-
A215559(n)={my(p=2^n-1);!for(d=0,n-2,forvec(v=vector(d,k,[2,n]),isprime(p-sum(i=1,d,2^(n-v[i])))|next;return(10^n\9-sum(i=1,d,10^(n-v[i]))),2))} \\ - M. F. Hasler, Aug 25 2012
A069672
Largest n-digit triangular number with minimum digit sum.
Original entry on oeis.org
1, 10, 300, 3003, 20100, 112101, 2001000, 33020001, 200010000, 3200120001, 20000100000, 320001200001, 2000001000000, 32000012000001, 200000010000000, 3200000120000001, 20000000100000000, 320000001200000001, 2000000001000000000, 32000000012000000001, 200000000010000000000, 3200000000120000000001, 20000000000100000000000, 320000000001200000000001, 2000000000001000000000000, 32000000000012000000000001, 200000000000010000000000000, 3200000000000120000000000001, 20000000000000100000000000000, 320000000000001200000000000001
Offset: 1
Cf.
A069661,
A069662,
A069663,
A069664,
A069665,
A069666,
A069667,
A069668,
A069669,
A069670,
A069671.
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F:= proc(d)
local s, P, nP, S, x, bestx;
bestx:= 0;
for s in [1,3,6,9] do
for P in map(op @combinat:-permute, combinat:-partition(s)) do
nP:= nops(P);
for S in map(t -> [d-1, op(t)], combinat:-choose([$0..d-2],nP-1)) do
x:= add(P[i]*10^S[i],i=1..nP);
if x > bestx and issqr(1+8*x) then bestx:= x fi;
od;
od;
if bestx > 0 then return bestx fi;
od;
end proc:
seq(F(d),d=1..30); # Robert Israel, May 25 2016
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