A033548 Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k.

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

Offset: 1

Author

Calculated by Jud McCranie

Keywords

• nonn
• base
• nice

Comments

A090431(A049084(a(n))) = 0.

Examples

			131 is the 32nd prime and sum of digits of both is 5.
		

References

• Proposed by G. L. Honaker, Jr.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A007605, A033549, A049084, A072439, A090431.

Programs

Haskell

a033548 n = a033548_list !! (n-1)
a033548_list = filter ((== 0) . a090431 . a049084) a000040_list
-- Reinhard Zumkeller, Mar 16 2014

Maple

read("transforms") :
isA033548 := proc(n)
    if isprime(n) and digsum(n) = digsum(numtheory[pi](n)) then
        true ;
    else
        false;
    end if;
end proc:
A033548 := proc(n)
    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:
seq(A033548(n),n=1..40) ; # R. J. Mathar, Jul 07 2021

Mathematica

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 *)

PARI

is(n)=isprime(n) && sumdigits(n)==sumdigits(primepi(n)) \\ Charles R Greathouse IV, Jun 18 2015

Python

from sympy.ntheory.factor_ import digits
from sympy import primepi, primerange
print([n for n in primerange(1, 5901) if (sum(digits(n)[1:])==sum(digits(primepi(n))[1:]))]) # Indranil Ghosh, Jun 27 2017, after Charles R Greathouse IV

Formula

a(n) = A000040(A033549(n)). - R. J. Mathar, Jul 07 2021

Extensions

More terms from Robert G. Wilson v, Jun 07 2009