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Primes p such that the smallest integer whose sum of decimal digits is p is prime.
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%I #15 Jul 28 2022 09:23:22

%S 2,3,5,7,11,17,19,23,29,31,41,43,71,79,97,173,179,257,269,311,389,691,

%T 4957,8423,11801,14621,25621,26951,38993,75743,102031,191671,668869

%N Primes p such that the smallest integer whose sum of decimal digits is p is prime.

%F Primes p such that (p mod 9 + 1) * 10^[p/9] - 1 is prime. Therefore the sequence consists of primes of the forms A002957(k)*9+1, A056703(k)*9+2, A056712(k)*9+4, A056716(k)*9+5, A056721(k)*9+7, A056725(k)*9+8. [_Max Alekseyev_, Nov 09 2009]

%e The smallest integer whose sum of digits is 17 is 89; 89 is prime, therefore 17 is in the sequence.

%t Select[Prime[Range[1000]],PrimeQ[FromDigits[Join[{Mod[ #,9]},Table[9,{i,1,Floor[ #/9]}]]]] &]

%o (Python)

%o from itertools import islice

%o from sympy import isprime, nextprime

%o def A051885(n): return ((n%9)+1)*10**(n//9)-1 # from _Chai Wah Wu_

%o def agen(startp=2):

%o p = startp

%o while True:

%o if isprime(A051885(p)): yield p

%o p = nextprime(p)

%o print(list(islice(agen(), 23))) # _Michael S. Branicky_, Jul 27 2022

%Y Cf. A051885.

%Y Cf. A002957, A056703, A056712, A056716, A056721, A056725.

%K hard,more,nonn,base

%O 1,1

%A _J. M. Bergot_, Jun 14 2007

%E Edited, corrected and extended by _Stefan Steinerberger_, Jun 23 2007

%E Extended by _D. S. McNeil_, Mar 20 2009

%E Five more terms from _Max Alekseyev_, Nov 09 2009