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A338877
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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.
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0
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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
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OFFSET
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1,1
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COMMENTS
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Primes in this sequence include 271639843 and 7245669763.
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LINKS
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EXAMPLE
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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)
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MAPLE
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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));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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