A054750 -id:A054750 - cp's OEIS frontend

A082257 Duplicate of A054750.

2, 3, 5, 7, 29, 67, 89, 199, 599, 2999, 4999, 29989, 59999, 79999, 389999, 989999

Offset: 1

dead

A067180 Smallest prime with digit sum n, or 0 if no such prime exists.

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

Offset: 1

Amarnath Murthy, Jan 09 2002

			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.

Robert Israel, Table of n, a(n) for n = 1..1000 (first 175 terms from Robert G. Wilson v)

Cf. A054750.

Removal of the 0 terms from this sequence leaves A067523.

g:= proc(s,d) # integers of <=d digits with sum s
  if s > 9*d then return [] fi;
  if d = 1 then return [s] fi;
  [seq(op(map(t -> j*10^(d-1)+ t, g(s-j,d-1))),j=0..9)];
end proc:
f:= proc(n) local d, j,x,y;
  if n mod 3 = 0 then return 0 fi;
  for d from ceil(n/9) do
    if d = 1 then
      if isprime(n) and n < 10 then return n
      else next
      fi
    fi;
    for j from 1 to 9 do
      for y in g(n-j,d-1) do
        x:= 10^(d-1)*j + y;
        if isprime(x) then return x fi;
  od od od;
end proc:
f(1):= 0: f(3):= 3:
map(f, [$1..100]); # Robert Israel, Dec 13 2020

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 *)

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

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

Edited and extended by Robert G. Wilson v, Mar 01 2002

Edited by Ray Chandler, Apr 24 2007

A075360 Smallest prime (> n-th prime) with sum of digits = the n-th prime, or 0 if no such prime exists.

Original entry on oeis.org

11, 0, 23, 43, 29, 67, 89, 199, 599, 2999, 4999, 29989, 59999, 79999, 389999, 989999, 6999899, 8989999, 59899999, 89999999, 289999999, 799999999, 3999998999, 19999997999, 79999999999, 399999998999, 599999899999, 999998999999

Offset: 1

Amarnath Murthy, Sep 19 2002

From a(5) onwards the sequence is same as A054750.

Cf. A054750.

A157712 Smallest prime made up of 0's and prime(n) 1's (or 0 when no such prime exists).

Original entry on oeis.org

11, 0, 101111, 11110111, 101111111111, 101101111111111, 101111111111111111, 1111111111111111111, 11111111111111111111111, 111110111111111111111111111111, 11111101111111111111111111111111

Offset: 1

Lekraj Beedassy, Mar 04 2009

Smallest prime with digit sum A000040(n) and using only 0's and 1's. Subsequence of A157709.

Chai Wah Wu, Table of n, a(n) for n = 1..168

Cf. A054750.

from _future_ import division
from itertools import combinations
from sympy import prime, isprime
def A157712(n):
    if n == 1:
        return 11
    if n == 2:
        return 0
    p = prime(n)
    l = p
    while True:
        for i in combinations(range(l),l-p):
            s = ['1']*l
            for x in i:
                s[x] = '0'
            q = int(''.join(s))
            if isprime(q):
                return q
        l += 1 # Chai Wah Wu, Nov 05 2015

Extended by Ray Chandler, Mar 06 2009

A161551 The smallest composite number larger than the n-th composite number, which has a sum of digits equal to the n-th composite number.

Original entry on oeis.org

22, 15, 26, 18, 28, 39, 68, 69, 88, 99, 299, 399, 589, 699, 799, 899, 999, 2899, 3999, 5999, 6999, 7999, 9899, 9999, 29999, 39999, 58999, 69999, 89999, 99999, 299899, 399999, 499999, 689999, 699999, 889999, 999999, 1999999, 3899999, 3999999

Offset: 1

Enoch Haga, Jun 13 2009

Variant of A073866, where the requirement that a(n) > A002808(n) is dropped.

			The first composite is 4, and the first sum of digits is 13, but since that is prime, we go to the next, 22, which being composite is a(1).

Cf. A075360, A054750.

A161551 := proc(n)
    for j from n+1 do
        if digsum(A002808(j)) = A002808(n) then
            return A002808(j) ;
        end if;
    end do:
end proc:
seq(A161551(n),n=1..30) ; # R. J. Mathar, Dec 06 2011

10 'compsdig, Enoch Haga, Jun 12 2009
20 N=1
30 Q=str(N)
40 L=len(Q)
50 for X=1 to L
60 M=str(mid(Q,X,1)): Z=Z+val(mid(Q,X,1))
70 next X
80 if Z=56 and Z<>prmdiv(Z) and N<>prmdiv(N) then print N: stop
90 Z=0: N=N+1: goto 30

min{c in A002808, c> A002808(n): A007953(c) = A002808(n)}. - R. J. Mathar, Dec 06 2011

A054797 Smallest prime number whose digits sum to the n-th palindromic prime.

Original entry on oeis.org

2, 3, 5, 7, 29, 399999998999, 789989999999999, 89989999999999999, 299999899999999999999, 4799999999999999999999, 88999999999999999999999999999999999, 3999899999999999999999999999999999999999, 689999999999999999999999999999999989999999, 6999989999999999999999999999999999999999999

Offset: 1

G. L. Honaker, Jr., Apr 27 2000

Dario Alejandro Alpern, Factorization using the Elliptic Curve Method
David Consiglio, Jr., C++ program for this sequence
Sean A. Irvine, Java program (GitHub)

Cf. A000040, A002385, A054750.

a(6) added by Carlos Rivera
a(7) from David Consiglio, Jr., Nov 07 2011
a(8)-a(14) from David Consiglio, Jr., Nov 16 2011
a(10) corrected by Sean A. Irvine, Feb 23 2022

A055019 Numbers n such that A051885(p_n) is prime, where p_n=A000040(n) is the n-th prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 20, 22, 25, 40, 41, 55, 57, 64, 77, 125, 663, 1053, 1414, 1711, 2822, 2956, 4107, 7463

Offset: 1

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 31 2000

Numbers n such that A051885(A000040(n)) = A054750(n).

No other terms below 10^4.

			The 125th prime is 691. The least integer with sum of digits 691 is A051885(691) = 8*10^76-1 which is prime. This is the 22nd prime with this property, so a(22)=125.

Cf. A054750, A051885.

for(X=1,300, a=prime(X)%9; b=prime(X)\9; m=(a+1)*10^b-1; if(isprime(m), print([X,prime(X),m]) ) )

More terms from Jason Earls, Jun 22 2001

a(27)-a(30) from Max Alekseyev, Dec 09 2011

A382461 a(n) is the smallest number whose sum of digits is 2^n.

Original entry on oeis.org

1, 2, 4, 8, 79, 5999, 19999999, 299999999999999, 49999999999999999999999999999, 899999999999999999999999999999999999999999999999999999999, 799999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Offset: 0

Stefano Spezia, Mar 27 2025

Cf. A000079, A007953, A051885, A054750, A060712, A136308, A180083.

a[n_]:=10^(Floor[2^n/9])(1+2^n-9Floor[2^n/9])-1; Array[a,11,0]

def A382461(n): return (lambda x:(x[1]+1)*10**x[0]-1)(divmod(1<Chai Wah Wu, Mar 29 2025

a(n) = 10^(floor(2^n/9))*(1 + 2^n - 9*floor(2^n/9)) - 1.

a(n) = A051885(2^n).

A161561 The smallest number larger than n with digital sum equal to n.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9999, 19999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 99999, 199999, 299999, 399999

Offset: 1

Enoch Haga, Jun 13 2009

			a(4)=13 because the sums of digits of the candidates 5 to 12 are all different from n=4, and 13 is the first candidate with sum 1+3 = n = 4.

Cf. A161551, A075360, A054750.

dsn[n_]:=Module[{k=n+1},While[Total[IntegerDigits[k]]!=n,k++];k]; Array[ dsn,50] (* Harvey P. Dale, Oct 24 2020 *)

a(n) = my(m = n+1); while(sumdigits(m) != n, m++); m; \\ Michel Marcus, Jun 08 2014

a(n) = min{k>n: A007953(k) = n}.

More precise definition from R. J. Mathar, Aug 30 2010

A346489 a(n) is the index of the smallest prime whose digits sum to n-th prime.

Original entry on oeis.org

1, 2, 3, 4, 10, 19, 24, 46, 109, 430, 669, 3245, 6057, 7837, 33067, 77777, 476643, 601855, 3556550, 5216954, 15739663, 41146179, 189961757, 882206624, 3325059246, 15581005618, 23007498153, 37607875618

Offset: 1

Ilya Gutkovskiy, Jul 19 2021

			a(10) = 430 because prime(430) = 2999, 2 + 9 + 9 + 9 = 29 = prime(10) and this is the smallest such number.

Cf. A000040, A000720, A007605, A028834, A046704, A046864, A054750, A075177.

Module[{nn=522*10^4,tbl},tbl=Table[{n,Total[IntegerDigits[Prime[n]]]},{n,nn}];Table[SelectFirst[tbl,#[[2]]==Prime[n]&],{n,20}]][[;;,1]] (* The program generates the first 20 terms of the sequence. *) (* Harvey P. Dale, Feb 19 2023 *)

a(n) = A000720(A054750(n)).

a(n) = min {k : A007605(k) = prime(n)}.

cp's OEIS Frontend

A082257 Duplicate of A054750.

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A067180 Smallest prime with digit sum n, or 0 if no such prime exists.

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A075360 Smallest prime (> n-th prime) with sum of digits = the n-th prime, or 0 if no such prime exists.

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A157712 Smallest prime made up of 0's and prime(n) 1's (or 0 when no such prime exists).

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A161551 The smallest composite number larger than the n-th composite number, which has a sum of digits equal to the n-th composite number.

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Maple

UBASIC

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A054797 Smallest prime number whose digits sum to the n-th palindromic prime.

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A055019 Numbers n such that A051885(p_n) is prime, where p_n=A000040(n) is the n-th prime.

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PARI

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A382461 a(n) is the smallest number whose sum of digits is 2^n.

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Mathematica

Python

Formula

A161561 The smallest number larger than n with digital sum equal to n.

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Programs

Mathematica

PARI