A236551 Primes formed from concatenation of PrimePi(n) and prime(n).

2, 13, 311, 313, 419, 641, 643, 647, 653, 761, 983, 997, 9103, 11131, 11149, 12157, 12163, 14197, 15227, 15233, 18307, 18311, 18313, 20353, 20359, 21379, 21383, 21397, 22409, 23431, 24499, 25523, 25541, 26557, 29599, 30631, 30643, 30661, 30677, 31727, 33773

Offset: 1

Author

K. D. Bajpai, Jan 28 2014

Keywords

• nonn
• base
• less

Examples

			pi(6) = 3: prime(6) = 13. Concatenation of 3 and 13 gives 313 which is prime and appears in the sequence.
pi(8) = 4: prime(6) = 19. Concatenation of 4 and 19 gives 419 which is prime and appears in the sequence.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1461

Crossrefs

Cf. A030458 (primes: concatenation of n and n+1), A084667 (primes: concatenation of n and prime(n)), A084669 (primes: concatenation of prime(n) and n).

Programs

Maple

with(StringTools): with(numtheory): KD := proc() local a,b,d; a:=pi(n); b:=ithprime(n); d:=parse(cat(a,b));  if isprime (d) then RETURN (d); fi;  end: seq(KD(), n=1..300);

Mathematica

Select[Table[FromDigits[Flatten[{IntegerDigits[PrimePi[n]], IntegerDigits[Prime[n]]}]], {n, 100}], PrimeQ] (* Alonso del Arte, Jan 28 2014 *)