A179634 Primes p such that p + d and p - d are primes, where d is the sum of floors of square roots of the digits of p.

5, 593, 647, 1097, 1187, 1367, 1453, 1663, 1753, 1783, 1873, 1907, 2287, 2377, 2417, 2683, 3463, 3637, 3923, 4513, 5413, 5807, 6263, 6317, 6373, 7523, 7823, 8087, 8117, 8237, 8713, 10853, 11807, 11833, 11903, 15313, 15803, 16063, 16223, 17027, 18223

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

647 is in the sequence since 647+(floor(sqrt(6))+floor(sqrt(4))+floor(sqrt(7))) = 647+(2+2+2) = 647+6 = 653 is prime AND 647-6 = 641 is prime.

Maple

filter:= proc(p) local L, t, d;
  if not isprime(p) then return false fi;
  L:= convert(p, base, 10);
  d:= add(floor(sqrt(t)), t=L);
  isprime(p-d) and isprime(p+d)
end proc:
select(filter, [seq(i, i=3..20000, 2)]); # Robert Israel, Apr 14 2020

Mathematica

Select[Prime[Range[2500]], With[{d = Total[Floor[Sqrt[IntegerDigits[#]]]]}, AllTrue[# + {d, -d}, PrimeQ]] &] (* Paolo Xausa, Jan 13 2026 *)

Prog

(PARI) isok(p) = isprime(p) && (d=digits(p)) && (sd = sum(i=1, #d, sqrtint(d[i]))) && isprime(p+sd) && isprime(p-sd); \\ Michel Marcus, Jan 19 2014

Crossrefs

Cf. A179632, A179633.

Sequence in context: A185555 A093941 A072952 * A302379 A303100 A302951

Adjacent sequences: A179631 A179632 A179633 * A179635 A179636 A179637

Keyword

nonn,base

Author

Carmine Suriano, Jul 21 2010

Extensions

Definition clarified by Robert Israel, Apr 14 2020

Status

approved