A106782 Primes with digit sum = 53.

989999, 1799999, 1889999, 1988999, 1989899, 1989989, 1997999, 1999799, 1999889, 1999979, 2699999, 2799899, 2799989, 2879999, 2899997, 2978999, 2979989, 2988899, 2989799, 2989997, 2998997, 2999879, 2999897, 3698999, 3789899

Offset: 1

Author

Zak Seidov, May 16 2005

Keywords

• nonn
• base

Comments

There are (1, 10, 23, 43, 87, 146, 255, 408, 642) terms below (1, 2, 3, ..., 9)*10^6. Among the 960 terms below 10^7, only {8998991, 8999981, 9899891, 9988991, 9997991, 9999971} end in the digit 1, only 30 end in the digit 3, and 268 end with a digit 7. - M. F. Hasler, Mar 09 2022

Links

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

Crossrefs

Cf. similar sequences listed in A244918.

Programs

Magma

[p: p in PrimesUpTo(3800000) | &+Intseq(p) eq 53]; // Vincenzo Librandi, Jul 09 2014

Mathematica

Select[Prime[Range[270000]],Total[IntegerDigits[#]]==53&]  (* Harvey P. Dale, Apr 17 2011 *)

PARI

select( {is_A106782(p)=sumdigits(p)==53&&isprime(p)}, primes([9e5,4e6]\1)) \\ M. F. Hasler, Mar 09 2022

Python

from itertools import count, islice
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def agen(b=10, sod=53): # 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(), 25))) # Michael S. Branicky, Mar 10 2022