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A077133
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a(n) is the difference between the sum of the first n even-indexed primes and the sum of the first n odd-indexed primes.
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5
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1, 3, 5, 7, 13, 19, 21, 27, 29, 33, 39, 45, 49, 53, 57, 61, 63, 65, 71, 77, 79, 81, 83, 95, 97, 103, 113, 119, 121, 125, 135, 139, 143, 149, 151, 157, 163, 167, 175, 183, 185, 187, 191, 199, 201, 213, 217, 221, 233, 251, 261, 267, 273, 279, 281, 287, 289, 299
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OFFSET
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1,2
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COMMENTS
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Some odd numbers such as 11, 17, 23 and 25 never appear.
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LINKS
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FORMULA
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a(n) = Sum_{i=0..n-1} (prime(2*i+2) - prime(2*i+1)).
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EXAMPLE
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a(2) = 3 as the sum of the first 2 even-indexed primes is prime(2) + prime(4) = 3 + 7 = 10, the sum of the first 2 odd-indexed primes is prime(1) + prime(3) = 2 + 5 = 7 and 10 - 7 = 3. [edited by Paolo Xausa, Apr 12 2023]
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MAPLE
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with(numtheory): A008347 := proc(n) option remember; if n = 0 then 0 else abs(A008347(n-1)-ithprime(n)); fi; end proc:
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MATHEMATICA
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Table[ Sum[ Prime[2i], {i, 1, n}] - Sum[ Prime[2i - 1], {i, 1, n}], {n, 1, 60}]
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PROG
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(PARI) my(pc=1, p1s=0, p2s=0); forprime (p=2, 500, pc=!pc; if (pc, p1s+=p, p2s+=p); if (pc, print1(p1s-p2s, ", ")))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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