0,1

n-deep nestings prime(prime(....(prime(k)..) = prime^n(k) can be arranged in a table T(n,k),

..2...3....5.....7....11....13 : A000040, n=0

..3...5...11....17....31....41 : A006450, n=1

..5..11...31....59...127...179 : A038580, n=2

.11..31..127...277...709..1063 : A049203

.31.127..709..1787..5381..8527 : A049202

127.709.5381.15299.52711.87803

a(n) is the leftmost value in the n-th row (the one with the smallest k) with a digit sum which is prime.

In order to generate the entries a(10) and a(11), prime2() was used which reads a large

880 gigabyte file of all primes < 10^12.

{min A000040^n(k): A000040^n(k) in A028834}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2009

0-th nesting is Prime(1) = 2 which has a prime digit sum: a(0). The 1st nesting is prime(prime(1)) = 3,

which has a prime digits sum: a(1)=3. The 2nd and 3rd nesting also succeed for k=1 while the fourth nesting

prime(prime(prime(prime(prime(4))))) = 1787 is the first occurrence of sum of

digits is prime. Here nesting for k= 1,2,3 does not sum to a prime number.

(PARI) for(j=0, 11, print(j", "sodip2(100, j)", "));

sodip2(n, m) = \\multiple nesting of prime(prime(prime..(n)

{

local(s=0, a, x, y, j, p);

for(x=1, n,

p=prime2(x);

for(i=1, m, p=prime2(p));

a=eval(Vec(Str(p)));

y=sum(j=1, length(a), a[j]);

if(isprime(y), return(p));

)

}

Sequence in context: A051835 A075883 A127814 this_sequence A112978 A002139 A140489

Adjacent sequences: A162250 A162251 A162252 this_sequence A162254 A162255 A162256

more,nonn

Cino Hilliard (hillcino368(AT)hotmail.com), Jun 29 2009

Definition rephrased by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2009