A284642 Numbers k such that concat(k, sigma(k)) and concat(sigma(k), k) are both prime.

1, 49, 961, 1089, 25281, 52441, 73441, 76729, 361201, 375769, 499849, 1315609, 1968409, 2961841, 3470769, 4289041, 4669921, 4748041, 5536609, 7392961, 7912969, 9296401, 9628609, 10556001, 13039321, 13830961, 14737921, 14753281, 17330569, 17380561, 18088009

Offset

1,2

Comments

All terms are odd squares. - Robert Israel, Apr 03 2017

Links

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

Example

sigma(49) = 57 and 5749 and 4957 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(sigma(n))+1)+sigma(n); b:=sigma(n)*10^(ilog10(n)+1)+n;
if isprime(a) and isprime(b) then print(n); fi; od; end: P(10^9);
# Alternative:
filter:= proc(n) local s;
  s:= numtheory:-sigma(n);
  isprime(n*10^(1+ilog10(s))+s) and isprime(s*10^(1+ilog10(n))+n)
end proc:
select(filter, [seq(i^2, i=1..10000, 2)]); # Robert Israel, Apr 03 2017

Mathematica

cnc[x_, y_] := FromDigits@ Flatten@ IntegerDigits[{x, y}]; Select[ Range[10^5], (d = DivisorSigma[1, #]; PrimeQ@ cnc[d, #] && PrimeQ@ cnc[#, d]) &] (* Giovanni Resta, Mar 31 2017 *)

Prog

(PARI)is(k)={my(v1=digits(k), v2=digits(sigma(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. A000203, A284643.

Sequence in context: A110906 A193940 A012115 * A304046 A264877 A173246

Adjacent sequences: A284639 A284640 A284641 * A284643 A284644 A284645

Keyword

nonn,base

Author

Paolo P. Lava, Mar 31 2017

Extensions

a(20)-a(31) from Giovanni Resta, Mar 31 2017

Status

approved