A246428 Primes p such that concatenation of the digit sum of p with p is also prime.

11, 19, 23, 29, 31, 41, 43, 53, 59, 61, 67, 89, 97, 113, 149, 151, 163, 173, 181, 211, 229, 233, 271, 293, 317, 331, 337, 347, 349, 353, 359, 379, 389, 419, 431, 433, 443, 449, 463, 467, 479, 521, 547, 563, 577, 599, 613, 619, 631, 653, 673, 683, 691, 739, 751

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..9400

Example

23 is in the sequence because it is prime; concatenation(2 + 3, 23) = 523 is also prime.
59 is in the sequence because it is prime; concatenation(5 + 9, 59) = 1459 is also prime.

Maple

with(StringTools): A246428 := proc() local a, b, d, e; a:=ithprime(m); b:=add( i, i = convert((a), base, 10))(a); d:=parse(cat(a, b)); e:= parse(cat(b, a)); if isprime(e) then RETURN (a); fi; end:
seq(A246428 (), m=1..300);

Mathematica

a246428[n_Integer] := Cases[Map[If[PrimeQ[FromDigits[Flatten[Append[List[Total[ IntegerDigits[ Prime[#]]]], IntegerDigits[Prime[#]]]]]] == True, Prime[#], False] &, Range[n]], _Integer]; a246428[135] (* Michael De Vlieger, Aug 07 2014 *)
Select[Prime[Range[200]], PrimeQ[FromDigits[Flatten[Join[{ IntegerDigits[ Total[ IntegerDigits[#]]], IntegerDigits[#]}]]]]&] (* Harvey P. Dale, Jan 12 2015 *)

Prog

(PARI)
for(n=1, 10^3, p=prime(n); if(isprime(eval(concat(Str(sumdigits(p)), Str(p)))), print1(p, ", "))) \\ Derek Orr, Jul 31 2014
(Python)
from sympy import prime, isprime
A246428 = [int(n) for n in (str(prime(x)) for x in range(1, 10**3))
          if isprime(int(str(sum([int(d) for d in n]))+n))]
# Chai Wah Wu, Aug 27 2014

Crossrefs

Cf. A245759, A245763.

Sequence in context: A374520 A335478 A136435 * A121658 A320867 A165947

Adjacent sequences: A246425 A246426 A246427 * A246429 A246430 A246431

Keyword

nonn,base

Author

K. D. Bajpai, Jul 31 2014

Status

approved