A386228 Primes that are the sum of prime factors (with multiplicity) of a triprime which is the concatenation of three consecutive primes.

8539, 11813, 19181, 27827, 45013, 52859, 64621, 64969, 81077, 103583, 105373, 127493, 228203, 264791, 297397, 318161, 324491, 439753, 466247, 480299, 491353, 496631, 561091, 613559, 638431, 678943, 779981, 822631, 827537, 906673, 908893, 1039477, 1046029, 1079927, 1090577, 1176871, 1220327

Offset

1,1

Comments

Numbers that are the sum of prime factors (with multiplicity) of at least one member of A385968.

Links

Robert Israel, Table of n, a(n) for n = 1..5098

Example

a(3) = 19181 is a term because 487491499 = A385968(4) is the concatenation of consecutive primes 487, 491, 499 and 487491499 = 11 * 2689 * 16481 with 11 + 2689 + 16481 = 19181 prime.
The only term < 3 * 10^9 that arises in more than one way is
a(756) = 149573911 = 53281 + 121110841 + 28409789
                 = 143597911 + 524453 + 5451547
where 53281 * 121110841 * 28409789 = 183325718332591833269 = A385968(3382)
and 143597911 * 524453 * 5451547 = 410557941055894105601 = A385968(6601).

Maple

tcat:= proc(a, b, c);
  c + 10^(1+ilog10(c))*(b + 10^(1+ilog10(b))*a)
end proc:
xmax:= 10^15: Bmax:= 3*10^6:
B:= NULL: count:= 0:
q:= 2: r:= 3:
do
  p:= q; q:= r; r:= nextprime(r);
  x:= tcat(p, q, r);
  if x > xmax then break fi;
  F:= ifactors(x)[2];
  if add(t[2], t=F) = 3 then
     b:= add(t[1]*t[2], t=F);
     if b <= Bmax and isprime(b) then
       count:= count+1; B:= B, b;
  fi fi;
od:
sort(convert({B}, list));

Crossrefs

Cf. A385968.

Sequence in context: A188214 A252810 A202986 * A297896 A217338 A217163

Adjacent sequences: A386225 A386226 A386227 * A386229 A386230 A386231

Keyword

nonn,base

Author

Will Gosnell and Robert Israel, Jul 15 2025

Status

approved