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A346501 With p = prime(n), a(n) is the least composite k such that A001414(k) = p and k+p is prime, or 0 if there is no such k. 1
0, 0, 6, 10, 48, 90, 210, 34, 416, 570, 58, 2652, 930, 1984, 1184, 1376, 2820, 118, 1062, 1830, 3660, 4020, 2190, 2370, 1602, 5340, 9006, 12702, 6208, 3090, 8502, 12198, 3810, 7620, 4448, 298, 21372, 17880, 4710, 15386, 7014, 21376, 22836, 11584, 11946, 394, 16548, 40596, 13926, 454, 7136, 6870 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
All terms are even.
Conjecture: a(n) > 0 for n >= 3.
LINKS
EXAMPLE
a(5) = 48 because A001414(48) = 11 = prime(5) and 48+11 = 59 is prime, and 48 is the least composite that works for this prime.
MAPLE
spf:= proc(n) local t;
add(t[1]*t[2], t=ifactors(n)[2])
end proc:
N:= 500: # for a(1)..a(N)
count:= 2:
V:= Vector(N):
for k from 4 by 2 while count < N do
if isprime(k) then next fi;
p:= spf(k);
if isprime(p) then
m:= numtheory:-pi(p);
if m <= N and V[m] = 0 and isprime(p+k) then
V[m]:= k; count:= count+1;
fi
fi
od:
convert(V, list);
MATHEMATICA
sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; seq[max_] := Module[{s = Table[0, {max}], c = 2, k = 3, p, ip}, While[c < max, k++; If[CompositeQ[k] && PrimeQ[(p = sopfr[k])] && PrimeQ[k + p] && (ip = PrimePi[p]) <= max && s[[ip]] == 0, c++; s[[ip]] = k]]; s]; seq[50] (* Amiram Eldar, Jul 22 2021 *)
PROG
(PARI) sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
a(n) = if (n<=2, return(0)); my(p=prime(n)); forcomposite(k=2, , if ((sopfr(k)==p) && isprime(k+p), return (k))); \\ Michel Marcus, Jul 22 2021
CROSSREFS
Cf. A001414.
Sequence in context: A068588 A083333 A032359 * A115917 A275004 A115741
KEYWORD
nonn,look
AUTHOR
J. M. Bergot and Robert Israel, Jul 20 2021
STATUS
approved

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Last modified May 22 13:22 EDT 2024. Contains 372755 sequences. (Running on oeis4.)