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 A238268 The number of unordered ways that n can be written as the sum of two numbers of the form p or 2p, where p is prime. 2
 1, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 5, 4, 4, 4, 5, 4, 4, 3, 4, 6, 4, 3, 7, 4, 3, 5, 6, 5, 5, 5, 6, 7, 4, 4, 9, 5, 5, 7, 6, 5, 5, 4, 5, 7, 4, 3, 10, 4, 4, 8, 8, 7, 7, 5, 6, 8, 5, 4, 10, 5, 5, 9, 8, 7, 8, 5, 7, 9, 5, 4, 13, 8, 6, 8, 8, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,3 COMMENTS p and 2p are terms of A001751. Sequence defined for n >= 4. It is conjectured that all terms of this sequence are greater than zero. LINKS Lei Zhou, Table of n, a(n) for n = 4..10000 EXAMPLE n=4, 4=2+2, one case found. So a(4)=1; ... n=24, 24 = 2+2*11 = 5+19 = 7+17 = 2*5+2*7 = 11+13, 5 cases found.  So a(24)=5; ... n=33, 33 = 2+31 = 2*2+29 = 7+2*13 = 2*5+23 = 11+2*11 = 2*7+19, 6 cases found.  So a(33)=6. MATHEMATICA Table[ct = 0; Do[If[((PrimeQ[i]) || (PrimeQ[i/2])) && ((PrimeQ[n - i]) || (PrimeQ[(n - i)/2])), ct++], {i, 2, Floor[n/2]}]; ct, {n, 4, 89}] PROG (PARI) isp(i) = isprime(i) || (((i % 2) == 0) && isprime(i/2)); a(n) = sum(i=1, n\2, isp(i) && isp(n-i)); \\ Michel Marcus, Mar 07 2014 CROSSREFS Cf. A001751, A002375, A103151. Sequence in context: A108133 A341120 A332252 * A194883 A328404 A175453 Adjacent sequences:  A238265 A238266 A238267 * A238269 A238270 A238271 KEYWORD nonn AUTHOR Lei Zhou, Feb 21 2014 STATUS approved

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Last modified June 19 12:55 EDT 2021. Contains 345129 sequences. (Running on oeis4.)