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A033548
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Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k.
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31
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131, 263, 457, 1039, 1049, 1091, 1301, 1361, 1433, 1571, 1913, 1933, 2141, 2221, 2273, 2441, 2591, 2663, 2707, 2719, 2729, 2803, 3067, 3137, 3229, 3433, 3559, 3631, 4091, 4153, 4357, 4397, 4703, 4723, 4903, 5009, 5507, 5701, 5711, 5741, 5801, 5843
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graph;
refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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LINKS
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FORMULA
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EXAMPLE
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131 is the 32nd prime and sum of digits of both is 5.
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MAPLE
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read("transforms") :
isA033548 := proc(n)
if isprime(n) and digsum(n) = digsum(numtheory[pi](n)) then
true ;
else
false;
end if;
end proc:
local p, k;
if n = 1 then
131;
else
p := nextprime(procname(n-1)) ;
while true do
if isA033548(p) then
return p;
end if;
p := nextprime(p) ;
end do:
end if;
end proc:
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MATHEMATICA
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Prime[ Select[ Range[ 2000 ], Apply[ Plus, IntegerDigits[ # ] ] == Apply[ Plus, IntegerDigits[ Prime[ # ] ] ] & ] ] (* Santi Spadaro, Oct 14 2001 *)
Select[ Prime@ Range@ 5927, Plus @@ IntegerDigits@ # == Plus @@ IntegerDigits@ PrimePi@ # &] (* Robert G. Wilson v, Jun 07 2009 *)
nn=800; Transpose[Select[Thread[{Prime[Range[nn]], Range[nn]}], Total[IntegerDigits[First[#]]]== Total[ IntegerDigits[ Last[#]]]&]][[1]] (* Harvey P. Dale, Jun 13 2011 *)
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PROG
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(Haskell)
a033548 n = a033548_list !! (n-1)
a033548_list = filter ((== 0) . a090431 . a049084) a000040_list
(Python)
from sympy.ntheory.factor_ import digits
from sympy import primepi, primerange
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CROSSREFS
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KEYWORD
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nonn,base,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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