A349455 Members of A014574 with sum of prime factors (with multiplicity) also in A014574.

4, 42, 60, 72, 618, 1488, 2730, 4230, 6762, 8010, 8232, 8538, 9282, 12540, 12822, 13008, 15582, 19212, 20898, 24420, 24918, 26712, 32718, 41412, 41610, 43542, 45318, 46830, 49530, 50130, 51060, 53172, 53550, 55662, 56598, 58230, 58368, 61560, 62130, 69930, 71712, 72090, 72222, 75402, 77688, 78192

Offset

1,1

Comments

Numbers k such that k-1, k+1, A001414(k)-1 and A001414(k)+1 are all prime.

Links

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

Example

a(3) = 60 is a term because 60-1 = 59 and 60+1 = 61 are primes, A001414(60) = 2+2+3+5 = 12, and 12-1 = 11 and 12+1 = 13 are primes.

Maple

spf:= proc(n) local F, t;
  F:= ifactors(n)[2];
  add(t[1]*t[2], t=F)
end proc:
R:= 4: count:= 1:
for t from 6 by 6 while count < 100 do
  if isprime(t-1) and isprime(t+1) then
    s:= spf(t);
    if isprime(s-1) and isprime(s+1) then
      count:= count+1;
      R:= R, t;
    fi
  fi
od:
R;

Mathematica

Select[Prime@Range@8000, PrimeQ[#+2]&&And@@PrimeQ[Total[Flatten[Table@@@FactorInteger[#+1]]]+{1, -1}]&]+1 (* Giorgos Kalogeropoulos, Nov 18 2021 *)

Crossrefs

Cf. A001414, A014574.

Sequence in context: A320335 A076652 A078288 * A089551 A347320 A220835

Adjacent sequences: A349452 A349453 A349454 * A349456 A349457 A349458

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 17 2021

Status

approved