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A067180 Smallest prime with digit sum n, or 0 if no such prime exists. 12
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, 2998999, 2999999, 0, 4999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

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

a(3k-2) =  A067523(2k-1), a(3k-1) = A067523(2k), for all k > 1. - M. F. Hasler, Nov 04 2018

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 *)

PROG

(PARI) A067180(n)={if(n<2, 0, n<4, n, n%3, my(d=divrem(n, 9)); forprime(p=d[2]*10^d[1]-1, , sumdigits(p)==n&&return(p)))} \\ M. F. Hasler, Nov 04 2018

CROSSREFS

Cf. A054750.

Removal of the 0 terms from this sequence 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 October 22 12:47 EDT 2019. Contains 328318 sequences. (Running on oeis4.)