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A267277 Zeroless primes p such that p*(product of digits of p)+(sum of digits of p) is also prime. 1
11, 13, 17, 19, 31, 37, 43, 47, 61, 73, 79, 83, 223, 227, 263, 281, 283, 463, 643, 683, 821, 827, 881, 1117, 1231, 1259, 1291, 1321, 1361, 1367, 1433, 1471, 1543, 1567, 1583, 1597, 1619, 1637, 1657, 1699, 1723, 1741, 1753, 1777, 1933, 1951, 1973 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Zeroless means that the decimal expansion has no digit "0", so no element of A056709 is in the sequence.

If we define a function "n*times products of digits plus sum of digits", f(n) = n*A007954(n) + A007953(n), then iterating the function starting at 217421 generates a chain of at least 4 primes: 217421 -> 24351169 -> 157795575151 -> 1522234189034803183.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

19 => 19*1*9+1+9 = 181 (is prime).

821 => 821*8*2*1+8+2+1 = 13147 (is prime).

2357 => 2357*2*3*5*7+2+3+5+7 = 494987 (is prime).

99995999 => 99995999*(9^7)*5+9*7+5 = 2391388816705223 (is prime).

MAPLE

isA267277 := proc(n)

    local pdgs ;

    if isprime(n) then

        pdgs := A007954(n) ;

        if pdgs <> 0 then

            isprime(n*pdgs+A007953(n)) ;

        else

            false;

        end if;

    else

        false;

    end if;

end proc:

for n from 1 to 400 do

    if isA267277(n) then

        printf("%d, \n", n);

    end if;

end do: # R. J. Mathar, Jan 16 2016

MATHEMATICA

Select[Prime@ Range@ 480, And[Last@ DigitCount@ # == 0, PrimeQ[Function[k, # Times @@ k + Total@ k]@ IntegerDigits@ #]] &] (* Michael De Vlieger, Jan 12 2016 *)

CROSSREFS

Cf. A007953, A007954, A038618, A056709.

Sequence in context: A168446 A275467 A045798 * A155071 A003626 A154981

Adjacent sequences:  A267274 A267275 A267276 * A267278 A267279 A267280

KEYWORD

nonn,base,less,easy

AUTHOR

Emre APARI, Jan 12 2016

STATUS

approved

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)