Original entry on oeis.org
11, 31, 41, 61, 71, 137, 193, 257, 467, 1399, 2887, 35999, 599699, 4987999, 589998989, 2899889999, 58989999989, 58799999999999, 579999998999999, 19999999999997999, 199999999999898999, 499999999999899989, 699999999999979999, 799999999999988999, 4999999999998899999, 7999999999998999899, 79999999999988999999
Offset: 1
a(2) = 31 because 31 is prime, and is the 4th (zero-free positive) number with digital sum 4 {4,13,22,31,112,121,211,1111}.
A081927
n-th positive integer whose digits sum up to n.
Original entry on oeis.org
1, 11, 21, 31, 41, 51, 61, 71, 81, 109, 137, 165, 193, 257, 294, 376, 467, 567, 676, 785, 894, 1399, 1778, 1986, 2887, 3869, 4869, 5878, 6887, 7896, 8959, 9968, 18798, 26998, 35999, 45999, 56899, 66989, 76998, 87799, 97889, 178899, 199798, 298988, 398988
Offset: 1
31 is the 4th integer of the sequence and the 4th number whose digits sum up to 4 : 4, 13, 22, [31], 103, 112, 121, 130, ...
109 is the 10th integer of the sequence and the 10th number whose digits sum up to 10 : 19, 28, 37, 46, 55, 64, 73, 82, 91, [109], 118, 127, 136, ...
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f:= proc(n) local Res, d, v, count;
count:= 0;
for d from ceil(n/9) while count < n do
v:= g(n,d,n-count,1);
Res:= v[-1];
count:= count + nops(v);
od:
Res
end proc:
g:= proc(n,d,remain) local rem, Res, j, j0, v;
if remain = 0 then return [] else rem:= remain fi;
if nargs = 4 then j0:= 1 else j0:= 0 fi;
if d = 1 then if n >= j0 and n <= 9 then [n] else [] fi
else
Res:= NULL;
for j from max(j0, ceil(n-9*(d-1))) to min(9,n) while rem > 0 do
v:= map(t -> j*10^(d-1)+t, procname(n-j,d-1,rem));
Res:= Res, op(v);
rem:= rem - nops(v);
od;
[Res]
fi
end proc:
map(f, [$1..200]); # Robert Israel, Feb 19 2018
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Table[Select[Range[500000],Total[IntegerDigits[#]]==n&][[n]],{n,45}] (* Harvey P. Dale, Mar 02 2024 *)
A181321
Primes with digital sum 70.
Original entry on oeis.org
189997999, 199799989, 199898899, 199997899, 199997989, 199998889, 268999999, 269998999, 278989999, 278999989, 279889999, 279988999, 287998999, 287999989, 288998989, 288999889, 288999979, 289699999, 289789999, 289889989
Offset: 1
Cf. similar sequences listed in
A244918.
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[p: p in PrimesUpTo(3*10^8) | &+Intseq(p) eq 70]; // Vincenzo Librandi, Jul 09 2014
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Select[Prime[Range[3*10^8]], Total[IntegerDigits[#]]==70 &] (* Vincenzo Librandi, Jul 09 2014 *)
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# see code in A107579 which can be used to produce this sequence by giving the initial term p = 189997999 (or 8*10**7-1, for digit sum 70). - M. F. Hasler, Mar 16 2022
A181181
Product of the first n zero-free positive numbers with digital sum n.
Original entry on oeis.org
1, 22, 756, 35464, 2112320, 152681760, 12984899200, 1270453824640, 140587147048320, 204867922610391040, 222308451584243548160, 277934723066170025856000, 385262452280397590195584000, 954777912911324324000159027200, 3057686768847576381964905048883200
Offset: 1
a(3) = 756 = 3 * 12 * 21.
a(4) = 35464 = 4 * 13 * 22 * 31.
a(5) = 2112320 = 5 * 14 * 23 * 32 * 41.
Showing 1-4 of 4 results.
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