A127272 - OEIS

%I #11 Jan 16 2023 11:15:20

%S 2,3,5,7,11,17,29,41,43,71,79,97,101,107,113,191,193,197,223,227,229,

%T 263,269,293,311,313,317,349,359,401,419,431,457,463,503,521,599,643,

%U 659,661,691,733,757,773,809,823,827,839,881,887,911,1013,1019,1021

%N Suppose the sum of the digits of prime(n) and prime(n+1) divides prime(n) + prime(n+1). Sequence gives prime(n).

%H Robert Israel, <a href="/A127272/b127272.txt">Table of n, a(n) for n = 1..10000</a>

%e Sum of the digits of prime(25) = 97 is 16, sum of the digits of prime(26) = 101 is 2. 16+2 = 18, which divides 97+101 = 198 = 11*18. Hence prime(25) = 97 is a term.

%p q:= 2: sq:= 2:

%p R:= NULL: count:= 0:

%p while count < 100 do

%p   p:= q; sp:= sq;

%p   q:= nextprime(q); sq:= convert(convert(q,base,10),`+`);

%p   if (p+q) mod (sp+sq) = 0 then

%p     R:= R,p; count:= count+1;

%p   fi

%p od:

%p R; # _Robert Israel_, Jan 15 2023

%t Prime[ Select[ Range[ 155 ], Mod[ Prime[ # ]+Prime[ #+1 ], Apply[ Plus, IntegerDigits[ Prime[ # ] ] ]+Apply[ Plus, IntegerDigits[ Prime[ #+1 ] ] ] ]==0& ] ] - Farideh Firoozbakht

%o (Magma) [ p: p in [ NthPrime(k): k in [1..172] ] | (p+q) mod (&+Intseq(p, 10) + &+Intseq(q, 10)) eq 0 where q is NextPrime(p) ]; /* _Klaus Brockhaus_, Mar 29 2007 */

%K nonn,base

%O 1,1

%A _J. M. Bergot_, Mar 27 2007

%E Edited and extended by _Klaus Brockhaus_ and _Farideh Firoozbakht_, Mar 29 2007