A162252 Numbers of the form prime(prime(prime(k))) with a digit sum which is prime.

5, 11, 179, 331, 599, 919, 1297, 1523, 1787, 2221, 3259, 3637, 3943, 4397, 5381, 6113, 6661, 6823, 8221, 9859, 10631, 11953, 12097, 12301, 12547, 12763, 13469, 14723, 15641, 15823, 17627, 18149, 19577, 20063, 20773, 21529, 23431, 26371, 26489

Offset: 1

Author

Cino Hilliard, Jun 28 2009

Keywords

• nonn
• base

Comments

Members of A038580 with a digit sum which is prime.

Examples

			For k=6, prime(prime(prime(6))) = A038580(6)=179. The digit sum 1+7+9 = 17 is prime, so 179 is in the sequence.
		

Programs

Maple

read("transforms") ; A038580 := proc(n) ithprime(ithprime(ithprime(n))) ; end:
for n from 1 to 80 do if isprime(digsum(A038580(n))) then printf("%d,", A038580(n)) ; fi; od: # R. J. Mathar, Aug 14 2009

Mathematica

Select[Table[Nest[Prime, x, 3], {x, 1, 100}],
PrimeQ[Total[IntegerDigits[#, 10]]] &]

PARI

sodip2(n,m) = /* m multiple nesting of prime(prime(prime..(n) */
{ local(s=0,a,x,y,j,p);
for(x=1,n, p=prime(x);
for(i=1,m,p=prime(p));
a=eval(Vec(Str(p))); y=sum(j=1,length(a),a[j]); if(isprime(y),print1(p","));)
}

Formula

{A038508(k): A007953(A038508(k)) in A000040, any k}.

Extensions

Edited by R. J. Mathar, Aug 14 2009