A321569 - OEIS

%I #15 Dec 28 2018 18:58:36

%S 23,1163,233,163,29,283,293,443,5233,67,4243,743,653,347,2239,439,

%T 1447,349,1367,683,449,7451,3881,929,1657,3257,15443,1567,11587,7723,

%U 2297,3259,4463,8237,2377,3727,9419,659,8951,2683,677,569,1867,2467,3583,2459,5743

%N Least prime p such that p plus the multiplication of its digits is the n-th prime after p.

%H Paolo P. Lava, <a href="/A321569/b321569.txt">Table of n, a(n) for n = 1..350</a>

%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_935.htm">Puzzle 935. pi+SOD(pi)=p(i+n)</a>, The Prime Puzzles and Problems Connection.

%e a(1) = 23 because 23 + 2*3 = 29 that is the first prime after 23.

%e a(2) = 1163 because 1163 + 1*1*6*3 = 1181 that is the second prime after 1163.

%p P:=proc(q) local k,n,p; for n from 1 to q do

%p for k from 1 to q do p:=ithprime(k);

%p if p+convert(convert(p,base,10),`*`)=ithprime(k+n) then lprint(n,p);

%p break; fi; od; od; end: P(10^9);

%t Array[Block[{p = 2}, While[p + Times @@ IntegerDigits@ p != NextPrime[p, #], p = NextPrime@ p]; p] &, 47] (* _Michael De Vlieger_, Dec 17 2018 *)

%Y Cf. A000040, A007954, A321568, A321570.

%K base,nonn,easy

%O 1,1

%A _Paolo P. Lava_, Dec 17 2018