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%I #14 May 09 2023 20:49:23
%S 173,383,431,443,461,491,521,563,761,821,827,839,941,971,983,1049,
%T 1481,1487,1493,1499,1553,1571,1601,1811,1871,1931,2153,2207,2477,
%U 2591,2609,2753,3037,3041,3083,3137,3221,3251,3257,3307,3329,3371
%N Primes p with no solution x to x=p*digitsum(x).
%C Primes p such that no number is p times its digit sum.
%C These may be called the non-Moran primes because no index k exists in A001101 to represent them as A001101(k)/digitsum[A001101(k)]. - _R. J. Mathar_, Aug 10 2007
%H David A. Corneth, <a href="/A130338/b130338.txt">Table of n, a(n) for n = 1..18497</a>
%F A000040 MINUS {A001101(k)/A007953(A001101(k)): k=1,2,3,4,..}. A003635 INTERSECT A000040. - _R. J. Mathar_, Aug 10 2007
%e p=5743 is not in the sequence because it can be represented as p=40201/7 (x=40201) or as p=80402/14 (x=80402).
%e p=7 is not in the sequence because it can be represented as p=21/3 (x=21) or p=42/6 (x=42) or p=63/9 (x=63) or p=84/12 (x=84). In all cases, the denominators are the digit sums of the numerators.
%p A007953 := proc(n) option remember ; add(j,j=convert(n,base,10)) ; end: A001101 := proc(p) option remember : local k,digs ; digs := 1; if not isprime(p) then RETURN(-1) ; else while 10^(digs-1)/(9*digs) <= p do for k from max(p,10^(digs-1)) to 10^digs do if k = p*A007953(k) then RETURN(k) ; fi ; od ; digs := digs+1 ; od: RETURN(-1) ; fi ; end: for n from 1 to 500 do if A001101(ithprime(n)) = -1 then printf("%d,",ithprime(n)) ; fi : od: # _R. J. Mathar_, Aug 10 2007
%o (Python)
%o from itertools import count, islice, combinations_with_replacement
%o from sympy import nextprime
%o def A130338_gen(startvalue=1): # generator of terms >= startvalue
%o n = nextprime(max(startvalue,1)-1)
%o while True:
%o for l in count(1):
%o if 9*l*n < 10**(l-1):
%o yield n
%o break
%o for d in combinations_with_replacement(range(10),l):
%o if (s:=sum(d))>0 and sorted(str(s*n)) == [str(e) for e in d]:
%o break
%o else:
%o continue
%o break
%o n = nextprime(n)
%o A130338_list = list(islice(A130338_gen(),20)) # _Chai Wah Wu_, May 09 2023
%Y Cf. A003635.
%Y Cf. A000040, A001101, A007953, A003635, A066007.
%K nonn,base
%O 1,1
%A _Lekraj Beedassy_, Aug 07 2007
%E More terms from _R. J. Mathar_, Aug 10 2007
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