A062341 -id:A062341 - cp's OEIS frontend

A133223 Sum of digits of primes (A007605), sorted and with duplicates removed.

2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103

Offset: 1

Lekraj Beedassy, Dec 19 2007

Presumably this is 3 together with numbers greater than 1 and not divisible by 3 (see A001651). - Charles R Greathouse IV, Jul 17 2013. (This is not a theorem because we do not know if, given s > 3 and not a multiple of 3, there is always a prime with digit-sum s. Cf. A067180, A067523. - N. J. A. Sloane, Nov 02 2018)
From Chai Wah Wu, Nov 04 2018: (Start)
Conjecture: for s > 10 and not a multiple of 3, there exists a prime with digit-sum s consisting only of the digits 2 and 3 (cf. A137269). This conjecture has been verified for s <= 2995.
Conjecture: for s > 18 and not a multiple of 3, there exists a prime with digit-sum s consisting only of the digits 3 and 4. This conjecture has been verified for s <= 1345.
Conjecture: for s > 90 and not a multiple of 3, there exists a prime with digit-sum s consisting only of the digits 8 and 9. This conjecture has been verified for s <= 8995.
Conjecture: for 0 < a < b < 10, gcd(a, b) = 1 and ab not a multiple of 10, if s > 90 and s is not a multiple of 3, then there exists a prime with digit-sum s consisting only of the digits a and b. (End)

Chai Wah Wu, Table of n, a(n) for n = 1..5997

Cf. A007605, A067523, A067180, A106754-A106787, A062339, A062341, A062337, A137269.

Corrected by Jeremy Gardiner, Feb 09 2014

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

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

Original entry on oeis.org

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

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

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A133223 Sum of digits of primes (A007605), sorted and with duplicates removed.

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

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

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

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Mathematica

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