A338877 Let g(p,k) = Sum_{0<=j<=k} p^j. Numbers that can be represented as g(p,k) and also as g(q,i)+g(r,j) with p,q,r prime and k,i,j>=2.

781, 1464, 5403, 36673, 49953, 13627173, 21330940, 34780507, 42009843, 81784893, 91231153, 119672661, 147902083, 271639843, 373784223, 522648183, 580400373, 684424083, 2716650763, 2827421103, 2955172683, 3495588253, 4006826701, 4144977543, 4215580257, 5109890773, 6163741591, 7245669763

Offset

1,1

Comments

Primes in this sequence include 271639843 and 7245669763.

Links

Table of n, a(n) for n=1..28.

Example

a(1) = 781 = g(5,4) = g(7,3) + g(19,2)
a(2) = 1464 = g(11,3) = g(37,2) + g(7,2)
a(3) = 5403 = g(73,2) = g(17,3) + g(13,2)
a(4) = 36673 = g(191,2) = g(2,14) + g(5,5)

Maple

N:= 10^10: # for terms <= N
S:= {}:
for p from 1 do
  p:= nextprime(p);
  if 1+p+p^2 > N then break fi;
  t:= 1+p;
  for k from 2 do
    t:= t+p^k;
    if t > N then break fi;
    S:= S union {t};
  od
od:
sort(convert(`union`(seq(map(`+`, S, S[i])) intersect S, i=1..nops(S)), list));

Crossrefs

Sequence in context: A250952 A139400 A115467 * A020231 A141390 A038477

Adjacent sequences: A338874 A338875 A338876 * A338878 A338879 A338880

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 06 2020

Status

approved