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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 17:11 EDT 2021. Contains 345049 sequences. (Running on oeis4.)