A069710 Primes with arithmetic mean of digits = 1 (sum of digits = number of digits).
11, 1021, 1201, 2011, 3001, 10103, 10211, 10301, 11003, 12011, 12101, 13001, 20021, 20201, 21011, 21101, 30011, 1000033, 1000213, 1000231, 1000303, 1001023, 1001041, 1001311, 1001401, 1002121, 1003003, 1003111, 1003201, 1010131
Offset: 1
Links
- David Radcliffe, Table of n, a(n) for n = 1..13376
Programs
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Maple
F:= proc(d,s) option remember; local t,r; if d = 1 then if s >= 1 and s <= 9 then {s} else {} fi else `union`(seq(map(t -> 10*t+r, procname(d-1,s-r)), r=0..min(s,9))) fi end proc: `union`(seq(select(isprime,F(i,i)), i = remove(d -> d mod 3 = 0, [$1..8])); # if using Maple 11 or earlier, uncomment the next line # sort(convert(%,list)); # Robert Israel, May 05 2015 -
Mathematica
Do[p = Prime[n]; If[ Apply[ Plus, IntegerDigits[p]] == Floor[ Log[10, p] + 1], Print[p]], {n, 1, 10^5}] -
Python
from itertools import count, islice from collections import Counter from sympy.utilities.iterables import partitions, multiset_permutations from sympy import isprime def A069710_gen(): # generator of terms for l in count(1): for i in range(1,min(9,l)+1): yield from sorted(q for q in (int(str(i)+''.join(map(str,j))) for s,p in partitions(l-i,k=9,size=True) for j in multiset_permutations([0]*(l-1-s)+list(Counter(p).elements()))) if isprime(q)) A069710_list = list(islice(A069710_gen(),30)) # Chai Wah Wu, Nov 28 2023
Extensions
Edited and extended by Robert G. Wilson v, Apr 12 2002
Comments