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

1,1

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)

Formula

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

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 *)

Prog

(Magma) [p: p in PrimesUpTo(10000) | &+Intseq(p) eq 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

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).

Sequence in context: A211821 A061237 A158293 * A245381 A050528 A257074

Adjacent sequences: A107576 A107577 A107578 * A107580 A107581 A107582

Keyword

nonn,base

Author

Zak Seidov, May 16 2005

Extensions

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

Status

approved