A247896 Primes that produce a different prime when one of its digits is added to it.

29, 43, 61, 67, 89, 167, 227, 239, 263, 269, 281, 349, 367, 389, 439, 457, 461, 463, 487, 499, 521, 563, 601, 607, 613, 641, 643, 647, 653, 677, 683, 821, 827, 983, 1063, 1229, 1277, 1283, 1289, 1361, 1367, 1423, 1427, 1429, 1447, 1481, 1483, 1489, 1549, 1601

Offset: 1

Author

Paolo P. Lava, Sep 26 2014

Keywords

• nonn
• easy
• base

Comments

From an idea of Eric Angelini (see seqfan link).

Digit 0 is not considered because the new primes must be different from the starting numbers. Therefore, 101 is not part of the sequence, because the only prime that results from adding one of its digits is 101 + 0 = 101, which is the same number, while 601 is acceptable because 601 + 6 = 607, a prime.

Examples

			The number 29 is prime, and 29 + 2 = 31 is also prime.
The same with 487, which produces 487 + 4 = 491, a prime.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000
• Eric Angelini, Primes adding one of their digit to themselves (+chains)

Crossrefs

Cf. A047791, A048519.

Cf. A000040, A010051.

Programs

Haskell

a247896 n = a247896_list !! (n-1)
a247896_list = filter f a000040_list where
   f p = any ((== 1) . a010051') $
             map (+ p) $ filter (> 0) $ map (read . return) $ show p
-- Reinhard Zumkeller, Sep 27 2014

Maple

P:=proc(q) local a,b,k,n,ok;
for n from 1 to q do a:=ithprime(n); ok:=0;
for k from 1 to ilog10(a)+1 do
b:=trunc((a mod 10^k)/10^(k-1)); if b>0 then
if isprime(a+b) then ok:=1; break; fi; fi; od;
if ok=1 then print(a); fi; od; end: P(10^6);

PARI

/* Description: Generates a vector containing this kind of terms between m^u1 and m^u2 for this definition applied by adding base B digits to the original number in decimal. Here (u1,m,B)=(1,3,10) by default. */
LstThem(u2,u1=1,m=3,B=10)={
  my(L:list=List(),y);
  forprime(x=m^u1,m^u2,
    y=vecsort(digits(x,B),,8);
    if(sum(j=1,#y,y[j]&&isprime(x+y[j])),
      listput(L,x)));
  vector(#L,i,L[i])} \\ R. J. Cano, Sep 27 2014