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

1,1

Comments

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

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)

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A142616 A207527 A132249 * A117477 A089316 A242846

Adjacent sequences: A033545 A033546 A033547 * A033549 A033550 A033551

Keyword

nonn,base,nice

Author

Calculated by Jud McCranie

Extensions

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

Status

approved