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A284643 Numbers k such that concat(k, d(k)) and concat(d(k), k) are both prime, where d(k) is the number of divisors of k. 3
1, 121, 169, 361, 1849, 14161, 17689, 25921, 41209, 51529, 52441, 64009, 69169, 76729, 124609, 187489, 247009, 436921, 776161, 851929, 935089, 1207801, 1951609, 2582449, 3179089, 3829849, 4363921, 4481689, 5094049, 6911641, 7382089, 7722841, 8116801, 8743849, 9186961 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that all terms are squares. - Michel Marcus, Apr 02 2017

All terms are odd squares, because k and d(k) must be odd. - Robert Israel, Apr 04 2017

LINKS

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

EXAMPLE

d(121) = 3 and 1213 and 3121 are both prime.

MAPLE

with(numtheory): P:=proc(q) local a, b, n; for n from 1 by 2 to q do

a:=n*10^(ilog10(tau(n))+1)+tau(n); b:=tau(n)*10^(ilog10(n)+1)+n;

if isprime(a) and isprime(b) then print(n); fi; od; end: P(10^9);

# Alternative:

filter:= proc(k) local d; d:= numtheory:-tau(k); isprime(d + 10^(1+ilog10(d))*k) and isprime(k+10^(1+ilog10(k))*d) end proc:

select(filter, [seq(k^2, k=1..10^4, 2)]); # Robert Israel, Apr 04 2017

MATHEMATICA

cnc[x_, y_] := FromDigits[Join @@ IntegerDigits@{x, y}]; Select[ Range[1, 5000, 2]^2, (t = DivisorSigma[0, #]; PrimeQ@ cnc[t, #] && PrimeQ@ cnc[#, t]) &] (* Giovanni Resta, Apr 04 2017 *)

PROG

(PARI) is(k)={my(v1=digits(k), v2=digits(numdiv(k))); isprime(fromdigits(concat(v1, v2)))&&isprime(fromdigits(concat(v2, v1)))};

findFirstTerms(q)={my(ans:list, k=1); ans=List(); q=max(1, q); for(c=1, q, while(!is(k), k++); listput(ans, k); k++); Vec(ans)} \\ R. J. Cano, Mar 31 2017

CROSSREFS

Cf. A000005, A065998.

Sequence in context: A258693 A037266 A240775 * A074730 A268519 A037050

Adjacent sequences:  A284640 A284641 A284642 * A284644 A284645 A284646

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Mar 31 2017

STATUS

approved

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Last modified October 16 08:40 EDT 2018. Contains 316259 sequences. (Running on oeis4.)