A107579 Primes with digit sum 10.

19, 37, 73, 109, 127, 163, 181, 271, 307, 433, 523, 541, 613, 631, 811, 1009, 1063, 1117, 1153, 1171, 1423, 1531, 1621, 1801, 2017, 2053, 2143, 2161, 2251, 2341, 2503, 2521, 3061, 3313, 3331, 3511, 4051, 4231, 5023, 5113, 6121, 6211, 6301, 8011, 8101

Offset: 1

Author

Zak Seidov, May 16 2005

Keywords

• nonn
• base

Comments

Subset of A061237 and A117674.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1001..3000 from Vincenzo Librandi and Zak Seidov, terms 1..1000 from Vincenzo Librandi)

Crossrefs

Cf. A000040 (primes), A007953 (sum of digits), A052224 (digit sum = 10).

Cf. A061237 (sum of digits == 1 (mod 9)).

Subsequence of A062340 (primes with digit sum divisible by 5).

Cf. A062339 (same for digit sum s = 4), A062341 (s = 5), A062343 (s = 8), A106754 (s = 11), and others listed in A244918 (s = 68).

Programs

Magma

[p: p in PrimesUpTo(10000) | &+Intseq(p) eq 10]; // Vincenzo Librandi, Jul 08 2014

Maple

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

Mathematica

Select[Prime[Range[100000]], Total[IntegerDigits[#]]==10 &] (* Vincenzo Librandi, Jul 08 2014 *)

PARI

forprime(p=19,8101,if(10==sumdigits(p),print(p","))) \\ Zak Seidov, Oct 08 2016

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

Python

from itertools import count, islice
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def agen(b=10, sod=10): # generator for any base, sum-of-digits
    if 0 <= sod < b:
        yield sod
    nzdigs = [i for i in range(1, b) if i <= sod]
    nzmultiset = []
    for d in range(1, b):
        nzmultiset += [d]*(sod//d)
    for d in count(2):
        fullmultiset = [0]*(d-1-(sod-1)//(b-1)) + nzmultiset
        for firstdig in nzdigs:
            target_sum, restmultiset = sod - int(firstdig), fullmultiset[:]
            restmultiset.remove(firstdig)
            for p in multiset_permutations(restmultiset, d-1):
                if sum(p) == target_sum:
                    t = int("".join(map(str, [firstdig]+p)), b)
                    if isprime(t):
                        yield t
                    if p[0] == target_sum:
                        break
print(list(islice(agen(), 45))) # Michael S. Branicky, Mar 10 2022

Python

from sympy import isprime
def A107579(p=19):
    "Return a generator of the sequence of all primes >= p with the same digit sum as p."
    while True:
        if isprime(p): yield p
        p = A228915(p) # skip to next larger integer with the same digit sum
a=A107579(); [next(a) for  in range(50)] # _M. F. Hasler, Mar 16 2022

Formula

Intersection of A000040 (primes) and A052224 (digit sum = 10). - M. F. Hasler, Mar 09 2022

Extensions

Edited by N. J. A. Sloane, Feb 20 2009 at the suggestion of Pacha Nambi