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A162253
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Smallest value of the n-fold nesting prime(prime(...(k)...) with a prime digital sum.
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0
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2, 3, 5, 11, 1787, 5381, 5381, 5381, 648391, 648391, 414507281407, 414507281407
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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(11) and a(12), prime2() was used which reads a large
880 gigabyte file of all primes < 10^12.
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FORMULA
| {min A000040^n(k): A000040^n(k) in A028834}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2009
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EXAMPLE
| 1-st nesting is prime(1) = 2 which has a prime digit sum: a(0). The second nesting is prime(prime(1)) = 3, which has a prime digits sum: a(1)=3. The 3rd and 4th nesting also succeed for k=1 while the fifth 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.
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PROG
| (PARI) for(j=1, 12, 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,
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));
)
}
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CROSSREFS
| Sequence in context: A075883 A195815 A127814 * A112978 A187129 A158936
Adjacent sequences: A162250 A162251 A162252 * A162254 A162255 A162256
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KEYWORD
| nonn,base,more
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Jun 29 2009
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EXTENSIONS
| Definition rephrased by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2009
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