A007605 -id:A007605 - cp's OEIS frontend

A090431 Difference between sums of digits of n and n-th prime.

-1, -1, -2, -3, 3, 2, -1, -2, 4, -10, -2, -7, -1, -2, -5, -1, -6, 2, -3, -6, -7, -12, -6, -11, -9, 6, 5, 2, 1, -2, -6, 0, -5, -6, -6, 2, -3, 1, -2, -7, -12, -4, -4, -5, -8, -9, 7, 5, 2, -8, -2, -7, 1, 1, -4, 0, -5, 3, -2, -5, -6, -6, -1, 5, 4, 1, 6, 1, 1, -9, -3, -8, -6, -2

Offset: 1

Reinhard Zumkeller, Dec 01 2003

a(n) = A007953(n) - A007605(n);

a(A033549(n))=a(A049084(A033548(n)))=0; a(A049084(A090432(n)))<0; a(A049084(A090433(n)))>0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A239324 (partial sums).

a090431 n = a007953 n - a007605 n  -- Reinhard Zumkeller, Mar 16 2014

A239619 Base 3 sum of digits of prime(n).

Original entry on oeis.org

2, 1, 3, 3, 3, 3, 5, 3, 5, 3, 3, 3, 5, 5, 5, 7, 5, 5, 5, 7, 5, 7, 3, 5, 5, 5, 5, 7, 3, 5, 5, 7, 5, 5, 7, 7, 7, 3, 5, 5, 7, 5, 5, 5, 7, 5, 7, 7, 7, 7, 9, 9, 9, 5, 5, 5, 7, 3, 5, 5, 5, 7, 5, 7, 7, 7, 5, 5, 7, 7, 5, 7, 7, 7, 5, 7, 7, 7, 9, 5, 7, 7, 9, 5, 7, 7, 9

Offset: 1

Tom Edgar, Mar 22 2014

			The fifth prime is 11, 11 in base 3 is (1,0,2) so a(5)=1+0+2=3.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A007605, A014499, A053735.

[&+Intseq(NthPrime(n),3): n in [1..100]]; // Vincenzo Librandi, Mar 25 2014

Table[Plus @@ IntegerDigits[Prime[n], 3], {n, 1, 100}] (* Vincenzo Librandi, Mar 25 2014 *)

a(n) = vecsum(digits(prime(n), 3)); \\ Michel Marcus, Mar 07 2020

[sum(i.digits(base=3)) for i in primes_first_n(200)]

a(n) = A053735(A000040(n)).

A239690 Base 4 sum of digits of prime(n).

Original entry on oeis.org

2, 3, 2, 4, 5, 4, 2, 4, 5, 5, 7, 4, 5, 7, 8, 5, 8, 7, 4, 5, 4, 7, 5, 5, 4, 5, 7, 8, 7, 5, 10, 5, 5, 7, 5, 7, 7, 7, 8, 8, 8, 7, 11, 4, 5, 7, 7, 10, 8, 7, 8, 11, 7, 11, 2, 5, 5, 7, 4, 5, 7, 5, 7, 8, 7, 8, 7, 4, 8, 7, 5, 8, 10, 7, 10, 11, 5, 7, 5, 7, 8, 7, 11, 7

Offset: 1

Tom Edgar, Mar 24 2014

a(n) is the rank of prime(n) in the base-4 dominance order on the natural numbers.

			The sixth prime is 13, 13 in base 4 is (3,1) so a(6)=3+1=4.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Tyler Ball and Daniel Juda, Dominance over N, Rose-Hulman Undergraduate Mathematics Journal, Vol. 13, No. 2, Fall 2013.

Cf. A007605, A014499, A053737, A239619.

Cf. A000040, A007090.

a239690 = a053737 . a000040  -- Reinhard Zumkeller, Mar 20 2015

[&+Intseq(NthPrime(n),4): n in [1..100]]; // Vincenzo Librandi, Mar 25 2014

Table[Plus @@ IntegerDigits[Prime[n], 4], {n, 1, 100}] (* Vincenzo Librandi, Mar 25 2014 *)

[sum(i.digits(base=4)) for i in primes_first_n(200)]

a(n) = A053737(A000040(n)).

A230199 Sum of digits of n-th palindromic prime.

Original entry on oeis.org

2, 3, 5, 7, 2, 2, 5, 7, 10, 11, 7, 11, 13, 14, 16, 19, 22, 23, 19, 20, 5, 7, 8, 7, 8, 10, 13, 14, 11, 16, 17, 13, 17, 16, 17, 14, 17, 19, 20, 20, 25, 19, 22, 23, 28, 29, 7, 8, 10, 13, 14, 8, 13, 13, 14, 17, 19, 22, 16, 17, 19, 23, 20, 23, 22, 25, 22, 23, 29

Offset: 1

Shyam Sunder Gupta, Oct 11 2013

			a(6) =2, since sum of digits of 6th palindromic prime i.e. 101 is 2.

Shyam Sunder Gupta, Table of n, a(n) for n = 1..5953

Cf. A002385, A007953, A007605.

a = {}; Do[z = n*10^(IntegerLength[n] - 1) +
FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[z], s = Apply[Plus, IntegerDigits[z]]; AppendTo[a, s]], {n, 1, 10^5}]; Insert[a, 2, 5]
palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; Total[ IntegerDigits[ #]]&/@ Select[Prime[Range[5000]],palQ] (* Harvey P. Dale, Oct 10 2014 *)

a(n) = A007953(A002385(n)). - R. J. Mathar, Sep 09 2015

A042939 Absolute values between digits of primes.

Original entry on oeis.org

2, 3, 5, 7, 0, 2, 6, 8, 1, 7, 2, 4, 3, 1, 3, 2, 4, 5, 1, 6, 4, 2, 5, 1, 2, 0, 2, 6, 8, 3, 8, 3, 9, 11, 12, 5, 11, 8, 12, 9, 15, 8, 9, 11, 15, 17, 0, 3, 7, 9, 4, 10, 3, 4, 10, 7, 13, 6, 12, 7, 9, 10, 4, 1, 1, 5, 1, 7, 8, 10, 5, 11, 10, 7, 13, 8, 14, 13, 3, 5, 6, 1, 0, 2, 8, 3, 9, 8, 3, 5, 9, 12, 11, 6

Offset: 1

Felice Russo

a(n) = absolute difference between the first digit of prime(n) and the sum of the other digits of prime(n). [Harvey P. Dale, Mar 11 2012]

James Spahlinger, Table of n, a(n) for n = 1..10000

Cf. A041000, A040164, A000040.

Cf. A007605.

a042939 = a040997 . a000040
-- Reinhard Zumkeller, Oct 10 2012

ddp[n_]:=Module[{idn=IntegerDigits[n]},Abs[First[idn]-Total[Rest[idn]]]]; ddp/@Prime[Range[100]] (* Harvey P. Dale, Mar 11 2012 *)

If decimal expansion of n-th prime is x1 x2 x3......xk then a(n)=|x1-x2-x3.......-xk|

a(n) = A040997(A000040(n)). - Reinhard Zumkeller, Oct 10 2012

A067523 The smallest prime with a possible given digit sum.

Original entry on oeis.org

2, 3, 13, 5, 7, 17, 19, 29, 67, 59, 79, 89, 199, 389, 499, 599, 997, 1889, 1999, 2999, 4999, 6899, 17989, 8999, 29989, 39989, 49999, 59999, 79999, 98999, 199999, 389999, 598999, 599999, 799999, 989999, 2998999, 2999999, 4999999, 6999899, 8989999

Offset: 1

Amarnath Murthy, Feb 14 2002

Except for 3 no other prime has a digit sum which is a multiple of 3. Hence the possible digit sums are 2,3,4,5,7,8,10,11,13,14,16,..., etc. Conjecture: For every possible digit sum there exists a prime.

For n > 2, this is (conjecturally) the smallest prime with digit sum A001651(n). - Lekraj Beedassy, Mar 04 2009

Robert Israel, Table of n, a(n) for n = 1..667

Cf. A001651. Equals A067180 with the 0 terms removed.

g:= proc(s, d) # integers of <=d digits with sum s
  local j;
  if s > 9*d then return [] fi;
  if d = 1 then return [s] fi;
  [seq(op(map(t -> j*10^(d-1)+ t, procname(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(3):= 3:
map(f, [2,3,seq(seq(3*i+j,j=1..2),i=1..30)]); # Robert Israel, Jan 18 2024

A067523(n)=if(n<3,n+1,A067180(n*3\/2-1)) \\ M. F. Hasler, Nov 04 2018

a(n) = min(prime(i): A007605(i) = A133223(i)). - R. J. Mathar, Nov 06 2018

More terms from Vladeta Jovovic, Feb 18 2002

Edited by Ray Chandler, Apr 24 2007

A073867 Smallest prime whose digital sum is equal to the n-th composite number, or 0 if no such prime exists.

Original entry on oeis.org

13, 0, 17, 0, 19, 0, 59, 0, 79, 0, 389, 0, 499, 0, 997, 1889, 0, 1999, 0, 6899, 0, 17989, 8999, 0, 39989, 0, 49999, 0, 98999, 0, 199999, 0, 598999, 599999, 0, 799999, 0, 2998999, 2999999, 0, 4999999, 0, 9899999, 0, 19999999, 29999999, 0, 59999999, 0

Offset: 1

Amarnath Murthy, Aug 15 2002

			The first composite number (A002808) is 4 and the least prime whose digital sum is 4 is 13.
The second composite number (A002808) is 6 whose digital sum is == 0 (mod 3) so there is no prime whose fits the definition.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Equals A067180(A002808(n)). Cf. A111397.

Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n]; f[n_] := Block[{cn = Composite[n]}, k = 1; While[Plus @@ IntegerDigits@Prime@k != cn, k++ ]; Prime[k]];

a(n)=0 iff that composite number (A002808(n)) is congruent to 0 (modulo 3), otherwise a(n)=A007605(k) for the first k that equals A002808(n).

a(19)-a(32) from Stefan Steinerberger, Nov 09 2005

a(33)-a(56) by Robert G. Wilson v, Nov 10 2005

A104250 Sum of prime digits of n-th prime.

Original entry on oeis.org

2, 3, 5, 7, 0, 3, 7, 0, 5, 2, 3, 10, 0, 3, 7, 8, 5, 0, 7, 7, 10, 7, 3, 0, 7, 0, 3, 7, 0, 3, 9, 3, 10, 3, 0, 5, 12, 3, 7, 10, 7, 0, 0, 3, 7, 0, 2, 7, 11, 4, 8, 5, 2, 7, 14, 5, 2, 9, 16, 2, 5, 5, 10, 3, 6, 10, 6, 13, 10, 3, 11, 8, 10, 13, 10, 6, 3, 10, 0, 0, 0, 2, 3, 6, 3, 3, 0, 12, 0, 3, 7, 7, 7, 0, 0, 8, 5

Offset: 1

Zak Seidov, Feb 26 2005

			a(6)=3 because sum of prime digits of Prime[6]=13 is 3.

Sum of nonprime digits (1, 4, 6, 8, 9) of n-th prime: A104251. Primes A000040: sum of digits of primes: A007605.

npd[n_]:=Total[Select[IntegerDigits[n],PrimeQ]]; Table[npd[p],{p,Prime[ Range[100]]}] (* Harvey P. Dale, Apr 24 2014 *)

a(n)=A007605(n)-A104251(n)

A106807 Primes with digit sum = 67.

Original entry on oeis.org

59899999, 69899899, 69899989, 69979999, 69997999, 69999799, 77899999, 78997999, 78998989, 78999889, 78999979, 79699999, 79879999, 79889899, 79979899, 79979989, 79988899, 79989979, 79996999, 79997899, 79997989

Offset: 1

Zak Seidov, May 18 2005

499999909 is the smallest term that contains 0 as a digit. - Altug Alkan, Mar 25 2018

Robert Israel, Table of n, a(n) for n = 1..10000 (first 128 terms from Vincenzo Librandi)

Cf. A007605, A062339, A062341, A062343, A106754 - A106787, A107617, A107618.

Cf. similar sequences listed in A244018.

[p: p in PrimesUpTo(90000000) | &+Intseq(p) eq 67]; // Vincenzo Librandi, Jul 09 2014

F:= proc(t,d)
  if d = 1 then
     if t<=9 then return [t] else return [] fi
  fi;
  if t > 9*d then return [] fi;
  [seq(op(map(x -> a*10^(d-1)+x, procname(t-a,d-1))), a=0..min(9,t))]
end proc:
select(isprime, F(67,8)); # Robert Israel, Mar 25 2018

Select[Prime[Range[600000]], Total[IntegerDigits[#]]==67 &] (* Vincenzo Librandi, Jul 09 2014 *)

isok(n) = isprime(n) && (sumdigits(n) == 67); \\ Altug Alkan, Mar 25 2018

A239691 Base 5 sum of digits of prime(n).

Original entry on oeis.org

2, 3, 1, 3, 3, 5, 5, 7, 7, 5, 3, 5, 5, 7, 7, 5, 7, 5, 7, 7, 9, 7, 7, 9, 9, 5, 7, 7, 9, 9, 3, 3, 5, 7, 9, 3, 5, 7, 7, 9, 7, 5, 7, 9, 9, 11, 7, 11, 7, 9, 9, 11, 9, 3, 5, 7, 9, 7, 5, 5, 7, 9, 7, 7, 9, 9, 7, 9, 11, 13, 9, 11, 11, 13, 7, 7, 9, 9, 5, 9, 11, 9, 7, 9

Offset: 1

Tom Edgar, Mar 24 2014

a(n) is the rank of prime(n) in the base-5 dominance order on the natural numbers.

			The fifth prime is 11, 11 in base 5 is (2,1) so a(5)=2+1=3.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Tyler Ball and Daniel Juda, Dominance over N, Rose-Hulman Undergraduate Mathematics Journal, Vol. 13, No. 2, Fall 2013.

Cf. A007605, A014499, A053824, A239690.

[&+Intseq(NthPrime(n),5): n in [1..100]]; // Vincenzo Librandi, Mar 25 2014

Table[Plus @@ IntegerDigits[Prime[n], 5], {n, 1, 100}] (* Vincenzo Librandi, Mar 25 2014 *)

a(n) = sumdigits(prime(n), 5); \\ Michel Marcus, Mar 04 2023

[sum(i.digits(base=5)) for i in primes_first_n(200)]

a(n) = A053824(A000040(n)).

cp's OEIS Frontend

A090431 Difference between sums of digits of n and n-th prime.

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A239619 Base 3 sum of digits of prime(n).

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A239690 Base 4 sum of digits of prime(n).

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A230199 Sum of digits of n-th palindromic prime.

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A042939 Absolute values between digits of primes.

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A067523 The smallest prime with a possible given digit sum.

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A073867 Smallest prime whose digital sum is equal to the n-th composite number, or 0 if no such prime exists.

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