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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 20 17:58 EST 2014. Contains 249754 sequences.