A127272 Suppose the sum of the digits of prime(n) and prime(n+1) divides prime(n) + prime(n+1). Sequence gives prime(n).

2, 3, 5, 7, 11, 17, 29, 41, 43, 71, 79, 97, 101, 107, 113, 191, 193, 197, 223, 227, 229, 263, 269, 293, 311, 313, 317, 349, 359, 401, 419, 431, 457, 463, 503, 521, 599, 643, 659, 661, 691, 733, 757, 773, 809, 823, 827, 839, 881, 887, 911, 1013, 1019, 1021

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

q:= 2: sq:= 2:
R:= NULL: count:= 0:
while count < 100 do
  p:= q; sp:= sq;
  q:= nextprime(q); sq:= convert(convert(q, base, 10), `+`);
  if (p+q) mod (sp+sq) = 0 then
    R:= R, p; count:= count+1;
  fi
od:
R; # Robert Israel, Jan 15 2023

Mathematica

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

Prog

(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 */

Crossrefs

Sequence in context: A052284 A133670 A356627 * A238528 A113192 A077673

Adjacent sequences: A127269 A127270 A127271 * A127273 A127274 A127275

Keyword

nonn,base

Author

J. M. Bergot, Mar 27 2007

Extensions

Edited and extended by Klaus Brockhaus and Farideh Firoozbakht, Mar 29 2007

Status

approved