

A067180


Smallest prime with digit sum n, or 0 if no such prime exists.


9



0, 2, 3, 13, 5, 0, 7, 17, 0, 19, 29, 0, 67, 59, 0, 79, 89, 0, 199, 389, 0, 499, 599, 0, 997, 1889, 0, 1999, 2999, 0, 4999, 6899, 0, 17989, 8999, 0, 29989, 39989, 0, 49999, 59999, 0, 79999, 98999, 0, 199999, 389999, 0, 598999, 599999, 0, 799999, 989999, 0
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OFFSET

1,2


COMMENTS

a(3k) = 0 for k>1.


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..175


EXAMPLE

a(68) = 59999999 because 59999999 is the smallest prime with digit sum = 68;
a(100) = 298999999999 because 298999999999 is the smallest prime with digit sum = 100.


MATHEMATICA

a = Table[0, {100}]; Do[b = Apply[ Plus, IntegerDigits[ Prime[n]]]; If[b < 101 && a[[b]] == 0, a[[b]] = Prime[n]], {n, 1, 10^7} ]; a
f[n_] := If[n > 5 && Mod[n, 3] == 0, 0, Block[{k = 1, lmt, lst = {}, ip = IntegerPartitions[n, Round[1 + n/9], {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}]}, lmt = 1 + Length@ ip; While[k < lmt, AppendTo[lst, Select[ FromDigits@# & /@ Permutations@ ip[[k]], PrimeQ[#] &]]; k++]; Min@ Flatten@ lst]]; f[1] = 0; f[4] = 13; Array[f, 70] (* Robert G. Wilson v, Sep 28 2014 *)


CROSSREFS

Cf. A054750.
Cf. Remove the 0 terms from this sequence and it leaves A067523.
Sequence in context: A196378 A051298 A069870 * A067182 A191000 A085402
Adjacent sequences: A067177 A067178 A067179 * A067181 A067182 A067183


KEYWORD

easy,nonn,base


AUTHOR

Amarnath Murthy, Jan 09 2002


EXTENSIONS

Edited and extended by Robert G. Wilson v, Mar 01 2002
Edited by Ray Chandler, Apr 24 2007


STATUS

approved



