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A107579 Primes with digit sum 10.

%I A107579 #41 Jan 19 2025 09:28:37
%S A107579 19,37,73,109,127,163,181,271,307,433,523,541,613,631,811,1009,1063,
%T A107579 1117,1153,1171,1423,1531,1621,1801,2017,2053,2143,2161,2251,2341,
%U A107579 2503,2521,3061,3313,3331,3511,4051,4231,5023,5113,6121,6211,6301,8011,8101
%N A107579 Primes with digit sum 10.
%C A107579 Subset of A061237 and A117674.
%H A107579 Michael S. Branicky, <a href="/A107579/b107579.txt">Table of n, a(n) for n = 1..10000</a> (terms 1001..3000 from Vincenzo Librandi and Zak Seidov, terms 1..1000 from Vincenzo Librandi)
%F A107579 Intersection of A000040 (primes) and A052224 (digit sum = 10). - _M. F. Hasler_, Mar 09 2022
%p A107579 a:=proc(n) local nn: nn:=convert(n,base,10): if isprime(n)=true and add(nn[j], j=1..nops(nn))=10 then n else end if end proc: seq(a(n),n=1..10^4); # _Emeric Deutsch_, Mar 06 2008
%t A107579 Select[Prime[Range[100000]], Total[IntegerDigits[#]]==10 &] (* _Vincenzo Librandi_, Jul 08 2014 *)
%o A107579 (Magma) [p: p in PrimesUpTo(10000) | &+Intseq(p) eq 10]; // _Vincenzo Librandi_, Jul 08 2014
%o A107579 (PARI) forprime(p=19,8101,if(10==sumdigits(p),print(p","))) \\ _Zak Seidov_, Oct 08 2016
%o A107579 (PARI) (A107579_nxt(p)=until(isprime(p=A228915(p)),); p); A107579_first(N=100)=vector(N, i, p=if(i>1, A107579_nxt(p), 19)) \\ _M. F. Hasler_, Mar 15 2022
%o A107579 (Python)
%o A107579 from itertools import count, islice
%o A107579 from sympy import isprime
%o A107579 from sympy.utilities.iterables import multiset_permutations
%o A107579 def agen(b=10, sod=10): # generator for any base, sum-of-digits
%o A107579     if 0 <= sod < b:
%o A107579         yield sod
%o A107579     nzdigs = [i for i in range(1, b) if i <= sod]
%o A107579     nzmultiset = []
%o A107579     for d in range(1, b):
%o A107579         nzmultiset += [d]*(sod//d)
%o A107579     for d in count(2):
%o A107579         fullmultiset = [0]*(d-1-(sod-1)//(b-1)) + nzmultiset
%o A107579         for firstdig in nzdigs:
%o A107579             target_sum, restmultiset = sod - int(firstdig), fullmultiset[:]
%o A107579             restmultiset.remove(firstdig)
%o A107579             for p in multiset_permutations(restmultiset, d-1):
%o A107579                 if sum(p) == target_sum:
%o A107579                     t = int("".join(map(str, [firstdig]+p)), b)
%o A107579                     if isprime(t):
%o A107579                         yield t
%o A107579                     if p[0] == target_sum:
%o A107579                         break
%o A107579 print(list(islice(agen(), 45))) # _Michael S. Branicky_, Mar 10 2022
%o A107579 (Python)
%o A107579 from sympy import isprime
%o A107579 def A107579(p=19):
%o A107579     "Return a generator of the sequence of all primes >= p with the same digit sum as p."
%o A107579     while True:
%o A107579         if isprime(p): yield p
%o A107579         p = A228915(p) # skip to next larger integer with the same digit sum
%o A107579 a=A107579(); [next(a) for _ in range(50)] # _M. F. Hasler_, Mar 16 2022
%Y A107579 Cf. A000040 (primes), A007953 (sum of digits), A052224 (digit sum = 10).
%Y A107579 Cf. A061237 (sum of digits == 1 (mod 9)).
%Y A107579 Subsequence of A062340 (primes with digit sum divisible by 5).
%Y A107579 Cf. A062339 (same for digit sum s = 4), A062341 (s = 5), A062343 (s = 8),  A106754 (s = 11), and others listed in A244918 (s = 68).
%K A107579 nonn,base
%O A107579 1,1
%A A107579 _Zak Seidov_, May 16 2005
%E A107579 Edited by _N. J. A. Sloane_, Feb 20 2009 at the suggestion of Pacha Nambi