A062339 -id:A062339 - cp's OEIS frontend

A158283 Prime numbers p such that 1 = abs(final digit of p - sum of all the other digits of p).

23, 43, 67, 89, 113, 157, 179, 199, 223, 269, 313, 337, 359, 379, 449, 607, 719, 739, 809, 829, 919, 1013, 1033, 1103, 1123, 1213, 1237, 1259, 1279, 1303, 1327, 1439, 1459, 1549, 1619, 1709, 2003, 2069, 2089, 2113, 2137, 2179, 2203, 2269, 2339, 2539

Offset: 1

Juri-Stepan Gerasimov, Mar 15 2009

			23(1=3-2), 43(1=abs(3-4)), 67(1=abs(7-6)), 89(1=abs(9-8)), 113(1=3-(1+1)).

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

Cf. A000040, A156979.

Cf. also A062339, A062341, A062337, A062343, A107579.

ps1[n_]:=Module[{idn=IntegerDigits[n]},Abs[Last[idn]-Total[Most[idn]]] == 1]; Select[Prime[Range[400]],ps1] (* Harvey P. Dale, Jul 31 2012 *)

Entries checked by R. J. Mathar, May 19 2010

A158571 Primes whose digit sum is a single-digit nonprime.

Original entry on oeis.org

13, 17, 31, 53, 71, 103, 107, 211, 233, 251, 431, 503, 521, 701, 1021, 1061, 1151, 1201, 1223, 1511, 1601, 2011, 2141, 2213, 2411, 3001, 3023, 3041, 3203, 3221, 4013, 4211, 5003, 5021, 6011, 6101, 7001, 10007, 10061, 10111, 10133, 10151, 10223, 10313

Offset: 1

Parthasarathy Nambi, Mar 21 2009

It is interesting to observe that it is hard to find (I found none) primes whose digit sum is 6. On the contrary, it is easier to find primes whose digit sum is 8.

The digit sum 6 does not occur here because a number with digit sum 6 is divisible by 3 and therefore not prime. - R. J. Mathar, Mar 26 2009

			1061 is a prime whose digit sum is 8, which is a single-digit nonprime.

Robert Israel, Table of n, a(n) for n = 1..10000
Chris Caldwell, The First 1,000 Primes

Cf. A158217.

for i from 1 to 8 do if member(i,[1,3,7]) then S[1,i]:= {i} else S[1,i]:= {} fi od:
for d from 2 to 5 do
  for x from 1 to 8 do
    S[d,x]:= {};
    for y from 0 to x-1 do
      S[d,x]:= S[d,x] union map(t -> 10^(d-1)*y + t, S[d-1,x-y])
od od od:
select(isprime, S[5,4] union S[5,8]); # Robert Israel, Apr 14 2021

Union of A062339 and A062343. - R. J. Mathar, Mar 26 2009

Extended by R. J. Mathar, Mar 26 2009

A165508 Numbers k such that 10^k + 111 is prime.

Original entry on oeis.org

2, 4, 184, 460, 784, 3248, 5194, 92386, 156428, 228208

Offset: 1

Rick L. Shepherd, Sep 21 2009

Terms must be congruent to 2 or 4 mod 6. Other than the first term, which produces 10^2 + 111 = 211, these terms produce primes whose decimal representation is 1  111 concatenated. These are only known to be highly probable primes for 184 and beyond. No more terms up to 15000.
a(8) > 55000. - Tyler NeSmith, Jul 10 2021
The corresponding primes have digit sum 4 (A062339). - Jeppe Stig Nielsen, Feb 10 2023
a(9) > 10^5. - Jeppe Stig Nielsen, Feb 11 2023
a(11) > 6.6*10^5. - Boyan Hu, Nov 14 2024

			As 10111 = 10^4 + 111 is a prime, 4 is a term.

Cf. A096912, A157711, A062339, A020449, A036929, A161786.

Select[Range[5200], PrimeQ[10^# + 111] &] (* G. C. Greubel, Oct 21 2018 *)

is(k)=ispseudoprime(10^k+111) \\ Charles R Greathouse IV, Jun 13 2017

a(8) from Jeppe Stig Nielsen, Feb 10 2023

a(9)-a(10) from Boyan Hu, Oct 23 2024

A168587 Smallest digit sum of an n-digit prime with only digits 0 and 1 (or 0, if no such prime exists).

Original entry on oeis.org

0, 2, 2, 0, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Lekraj Beedassy, Nov 30 2009

See A168586 for the corresponding primes.

Cf. A062339.

Extended by Ray Chandler, Dec 03 2009

A382073 Semiprimes with sum of digits 4.

Original entry on oeis.org

4, 22, 121, 202, 301, 1003, 1111, 2101, 10003, 10021, 10102, 10201, 11002, 11101, 12001, 30001, 100021, 100102, 100201, 101011, 110002, 110101, 111001, 200011, 200101, 1000021, 1000111, 1000201, 1001002, 1001101, 1110001, 2001001, 3000001, 10000003, 10000021, 10000201, 10010002, 10020001

Offset: 1

Zak Seidov and Robert Israel, Mar 14 2025

			a(3) = 121 is a term because 121 = 11^2 is a semiprime and its sum of digits is 1+2+1=4.

Robert Israel, Table of n, a(n) for n = 1..3655

Intersection of A001358 and A052218.

Cf. A062339.

qsemi:= proc(n) if numtheory:-bigomega(n) = 2 then n fi end proc:
F:= proc(d) local i,j;
   seq(seq(qsemi(10^(d-1)+1 + 10^i + 10^j),i=0..j),j=0..d-1)
end proc:
map(F, [$1..10]);

Select[Range[10^5],PrimeOmega[#]==2 && DigitSum[#]==4 &] (* Stefano Spezia, Mar 14 2025 *)

A157715 Primes sorted on digit sums, then on the primes.

Original entry on oeis.org

2, 11, 101, 3, 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

Offset: 1

Lekraj Beedassy, Mar 04 2009

Beyond n = 4, a(n) is believed to coincide with A062339.

Only correct for n >= 4 if an undiscovered prime of digit sum two (which would have to be a member of A080176) does not exist; this is conjectured but not proved. - Jeppe Stig Nielsen, Mar 30 2018

			There are only three primes with a digit sum of 2, and those are 2, 11, 101. Therefore these three primes are the first three terms of this sequence.
There is only one prime with a digit sum of 3, and that's 3 itself. Any higher number with a digit sum of 3 is a nontrivial multiple of 3 and therefore composite.
Then follows the first prime with a digit sum of 4, which is 13.

Cf. A062341.

Prime@ Flatten@ Values@ Take[KeySort@ PositionIndex[Total@ IntegerDigits@ # & /@ Prime@ Range[10^7]], 3] (* Michael De Vlieger, Apr 07 2018 *)

Comment edited by Robert Israel, Dec 28 2015

A294396 Numbers k such that 12*10^k + 1 is prime.

Original entry on oeis.org

0, 2, 38, 80, 9230, 25598, 39500

Offset: 1

Patrick A. Thomas, Feb 12 2018

k must be even since 12*10^k + 1 is divisible by 11 if k is odd. - Robert G. Wilson v, Feb 12 2018
a(7) > 27440. - Robert G. Wilson v, Feb 17 2018
a(8) > 10^5. - Jeppe Stig Nielsen, Jan 31 2023

			13 and 1201 are prime, so 0 and 2 are the initial values.

Cf. A001562, A096507, A056797, A056807, A056806, A102940, A056805, A056804, A096508, A102975, A289051, A099017, A295325, A273002, A102945, A282456, A267420.

Cf. A062339 (primes with digit sum 4).

ParallelMap[ If[ PrimeQ[12*10^# +1], #, Nothing] &, 2 + 6Range@ 4500] (* Robert G. Wilson v, Feb 13 2018 *)

isok(k) = isprime(12*10^k + 1); \\ Altug Alkan, Mar 04 2018

a(5) from Robert G. Wilson v, Feb 12 2018
a(6) from Robert G. Wilson v, Feb 13 2018
a(7) from Jeppe Stig Nielsen, Jan 28 2023

cp's OEIS Frontend

A158283 Prime numbers p such that 1 = abs(final digit of p - sum of all the other digits of p).

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A158571 Primes whose digit sum is a single-digit nonprime.

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A165508 Numbers k such that 10^k + 111 is prime.

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A168587 Smallest digit sum of an n-digit prime with only digits 0 and 1 (or 0, if no such prime exists).

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A382073 Semiprimes with sum of digits 4.

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A157715 Primes sorted on digit sums, then on the primes.

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A294396 Numbers k such that 12*10^k + 1 is prime.

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Mathematica

PARI

Extensions