A106763 -id:A106763 - cp's OEIS frontend

A244918 Primes p where the digital sum is equal to 68.

59999999, 69999899, 69999989, 78998999, 88989899, 88999979, 89699999, 89799989, 89989799, 89989979, 89997899, 89997989, 89999699, 89999969, 97889999, 98699999, 98879999, 98899799, 98979989, 98988899, 98989889, 98997989, 98998979, 98999969

Offset: 1

Vincenzo Librandi, Jul 08 2014

			69999899 is a prime with sum of the digits = 68, hence belongs to the sequence.

Vincenzo Librandi and Chai Wah Wu, Table of n, a(n) for n = 1..10000 n = 1..45 from Vincenzo Librandi.

Cf. Primes p where the digital sum is equal to k: 2, 11 and 101 for k=2; A062339 (k=4), A062341 (k=5), A062337 (k=7), A062343 (k=8), A107579 (k=10), A106754 (k=11), A106755 (k=13), A106756 (k=14), A106757 (k=16), A106758 (k=17), A106759 (k=19), A106760 (k=20), A106761 (k=22), A106762 (k=23), A106763 (k=25), A106764 (k=26), A048517 (k=28), A106766 (k=29), A106767 (k=31), A106768 (k=32), A106769 (k=34), A106770 (k=35), A106771 (k=37), A106772 (k=38), A106773 (k=40), A106774 (k=41), A106775 (k=43), A106776 (k=44), A106777 (k=46), A106778 (k=47), A106779 (k=49), A106780 (k=50), A106781 (k=52), A106782 (k=53), A106783 (k=55), A106784 (k=56), A106785 (k=58), A106786 (k=59), A106787 (k=61), A107617 (k=62), A107618 (k=64), A107619 (k=65), A106807 (k=67), this sequence (k=68), A181321 (k=70).

[p: p in PrimesUpTo(100000000) | &+Intseq(p) eq 68];

Select[Prime[Range[10000000]], Total[IntegerDigits[#]]==68 &]

# see code in A107579: the same code can be used to produce this sequence, by giving the initial term p = 6*10**7-1, for digit sum 68. - M. F. Hasler, Mar 16 2022

A062339 Primes whose sum of digits is 4.

Original entry on oeis.org

13, 31, 103, 211, 1021, 1201, 2011, 3001, 10111, 20011, 20101, 21001, 100003, 102001, 1000003, 1011001, 1020001, 1100101, 2100001, 10010101, 10100011, 20001001, 30000001, 101001001, 200001001, 1000000021, 1000001011, 1000010101, 1000020001, 1000200001, 1002000001, 1010000011

Offset: 1

Amarnath Murthy, Jun 21 2001

Is this sequence (and its brothers A062337, A062341 and A062343) infinite?

10^A049054(m)+3 and 3*10^A056807(m)+1 are subsequences. A107715 (primes containing only digits from set {0,1,2,3}) is a supersequence. Terms not containing the digit 3 are either terms of A020449 (primes that contain digits 0 and 1 only) or of A106100 (primes with maximal digit 2) - and thus terms of these sequences' union A036953 (primes containing only digits from set {0,1,2}). - Rick L. Shepherd, May 23 2005

			3001 is a prime with sum of digits = 4, hence belongs to the sequence.

T. D. Noe and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..1000 from T. D. Noe)
Amin Witno, Numbers which factor as their digital sum times a prime, International Journal of Open Problems in Computer Science and Mathematics 3:2 (2010), pp. 132-136.

Subsequence of A062338, A107288, and A107715 (primes with digits <= 3).
A159352 is a subsequence.
Cf. A000040 (primes), A052218 (digit sum = 4), A061239 (primes == 4 (mod 9)).
Cf. Primes p with digital sum equal to k: {2, 11 and 101} for k=2; this sequence (k=4), A062341 (k=5), A062337 (k=7), A062343 (k=8), A107579 (k=10), A106754 (k=11), A106755 (k=13), A106756 (k=14), A106757 (k=16), A106758 (k=17), A106759 (k=19), A106760 (k=20), A106761 (k=22), A106762 (k=23), A106763 (k=25), A106764 (k=26), A048517 (k=28), A106766 (k=29), A106767 (k=31), A106768 (k=32), A106769 (k=34), A106770 (k=35), A106771 (k=37), A106772 (k=38), A106773 (k=40), A106774 (k=41), A106775 (k=43), A106776 (k=44), A106777 (k=46), A106778 (k=47), A106779 (k=49), A106780 (k=50), A106781 (k=52), A106782 (k=53), A106783 (k=55), A106784 (k=56), A106785 (k=58), A106786 (k=59), A106787 (k=61), A107617 (k=62), A107618 (k=64), A107619 (k=65), A106807 (k=67), A244918 (k=68), A181321 (k=70).
Cf. A049054 (10^k+3 is prime), A159352 (these primes).
Cf. A056807 (3*10^k+1 is prime), A259866 (these primes).
Cf. A020449 (primes with digits 0 and 1), A036953 (primes with digits <= 2), A106100 (primes with largest digit = 2), A069663, A069664 (smallest resp. largest n-digit prime with minimum digit sum).

[p: p in PrimesUpTo(800000000) | &+Intseq(p) eq 4]; // Vincenzo Librandi, Jul 08 2014

N:= 20: # to get all terms < 10^N
B[1]:= {1}:
B[2]:= {2}:
B[3]:= {3}:
A:= {}:
for d from 2 to N do
   B[4]:= map(t -> 10*t+1,B[3]) union  map(t -> 10*t+3,B[1]);
   B[3]:= map(t -> 10*t, B[3]) union map(t -> 10*t+1,B[2]) union map(t -> 10*t+2,B[1]);
   B[2]:= map(t -> 10*t, B[2]) union map(t -> 10*t+1,B[1]);
   B[1]:= map(t -> 10*t, B[1]);
   A:= A union select(isprime,B[4]);
od:
sort(convert(A,list)); # Robert Israel, Dec 28 2015

Union[FromDigits/@Select[Flatten[Table[Tuples[{0,1,2,3},k],{k,9}],1],PrimeQ[FromDigits[#]]&&Total[#]==4&]] (* Jayanta Basu, May 19 2013 *)
FromDigits/@Select[Tuples[{0,1,2,3},10],Total[#]==4&&PrimeQ[FromDigits[#]]&] (* Harvey P. Dale, Jul 23 2025 *)

for(a=1,20,for(b=0,a,for(c=0,b,if(isprime(k=10^a+10^b+10^c+1),print1(k", "))))) \\ Charles R Greathouse IV, Jul 26 2011

select( {is_A062339(p,s=4)=sumdigits(p)==s&&isprime(p)}, primes([1,10^7])) \\ 2nd optional parameter for similar sequences with other digit sums. M. F. Hasler, Mar 09 2022

A062339_upto_length(L,s=4,a=List(),u=[10^(L-k)|k<-[1..L]])=forvec(d=[[1,L]|i<-[1..s]], isprime(p=vecsum(vecextract(u,d))) && listput(a,p),1); Vecrev(a) \\ M. F. Hasler, Mar 09 2022

Intersection of A052218 (digit sum 4) and A000040 (primes). - M. F. Hasler, Mar 09 2022

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 06 2001
More terms from Rick L. Shepherd, May 23 2005
More terms from Lekraj Beedassy, Dec 19 2007

A062340 Primes whose sum of digits is a multiple of 5.

Original entry on oeis.org

5, 19, 23, 37, 41, 73, 109, 113, 127, 131, 163, 181, 271, 307, 311, 389, 401, 433, 479, 523, 541, 569, 587, 613, 631, 659, 677, 811, 839, 857, 929, 947, 983, 997, 1009, 1013, 1031, 1063, 1103, 1117, 1153, 1171, 1289, 1301, 1423, 1487, 1531, 1559, 1621, 1667

Offset: 1

Amarnath Murthy, Jun 21 2001

			569 is a prime with sum of digits = 20, hence belongs to the sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A007953 (sum of digits), A227793 (sum of digits divisible by 5).
Has as subsequence A062341 (primes with sum of digits s = 5), A107579 (s = 10), A106760 (s = 20), A106763 (s = 25), A106770 (s = 35), A106773 (s = 40), A106780 (s = 50), A106783 (s = 55), A107619 (s = 65) and A181321 (s = 70).
Cf. A062340 (equivalent for 8).

[ p: p in PrimesUpTo(10000) | &+Intseq(p) mod 5 eq 0 ]; // Vincenzo Librandi, Apr 02 2011

Select[Prime[Range[300]],Divisible[Total[IntegerDigits[#]],5]&] (* Harvey P. Dale, Jul 06 2020 *)

select( {is_A062340(n)=sumdigits(n)%5==0&&isprime(n)}, primes([1,2000])) \\ M. F. Hasler, Mar 10 2022

from sympy import primerange as primes
def ok(p): return sum(map(int, str(p)))%5 == 0
print(list(filter(ok, primes(1, 1668)))) # Michael S. Branicky, May 19 2021

Intersection of A000040 (primes) and A227793 (sum of digits in 5Z). - M. F. Hasler, Mar 10 2022

Corrected and extended by Harvey P. Dale and Larry Reeves (larryr(AT)acm.org), Jul 04 2001

A247122 Primes p such that the digit sum of p is an odd composite number.

Original entry on oeis.org

997, 1699, 1789, 1879, 1987, 2689, 2797, 2887, 3499, 3697, 3769, 3877, 3967, 4597, 4759, 4957, 4993, 5479, 5569, 5659, 5749, 5839, 5857, 6199, 6379, 6397, 6469, 6577, 6793, 6829, 6883, 6991, 7297, 7369, 7459, 7477, 7549, 7639, 7873, 7927, 7963, 8089, 8179, 8269, 8287, 8377, 8467, 8539, 8629, 8647, 8719, 8737, 8863, 8971, 8999

Offset: 1

Derek Orr, Nov 19 2014

Motivation from James Grime: "What is the smallest prime with digital sum odd, but not prime?"
This sequences differs from A106763 at a(55) = 8999.
The digit sums are multiples of primes > 3. If the digit sum is a multiple of 3, the number itself cannot be prime.
The first odd composite digit sums are 25 (first occurrence is for 997), 35 (first occurrence is for 8999), 49 (first occurrence is for 598999), 55 (first occurrence is for 2998999), 65 (first occurrence is for 29999999), 77 (first occurrence is for 699899999) ...

			997 is prime but its digit sum is 25, which is odd and composite. So 997 is a member of this sequence.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A106763, A007953.

a247122[n_Integer] := Flatten@Last@Reap[Module[{i, digitSum}, digitSum[x_] := Plus @@ IntegerDigits[x]; For[i = 1, i < n,
If[OddQ[digitSum[Prime[i]]] && CompositeQ[digitSum[Prime[i]]],
Sow[Prime[i]], Null], i++]]]; a247122[1200] (* Michael De Vlieger, Nov 29 2014 *)
dsocQ[n_]:=Module[{s=Total[IntegerDigits[n]]},OddQ[s]&&CompositeQ[s]]; Select[Prime[Range[1200]],dsocQ] (* Harvey P. Dale, Feb 21 2016 *)

forprime(p=1,10^4,if(!isprime(sumdigits(p))&&sumdigits(p)%2,print1(p,", ")))

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A244918 Primes p where the digital sum is equal to 68.

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A062339 Primes whose sum of digits is 4.

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A062340 Primes whose sum of digits is a multiple of 5.

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Magma

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A247122 Primes p such that the digit sum of p is an odd composite number.

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Mathematica

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