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

Author

Will Gosnell and Robert Israel, Jul 15 2025

Keywords

• nonn
• base

Comments

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

Examples

			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).
		

Links

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

Crossrefs

Cf. A385968.

Programs

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));