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 A288949 Numbers that are both the sum of two consecutive primes and the sum of two consecutive semiprimes. 1
 24, 36, 100, 112, 120, 240, 288, 320, 372, 472, 532, 576, 600, 810, 828, 864, 882, 924, 990, 1088, 1104, 1164, 1180, 1208, 1236, 1284, 1360, 1392, 1482, 1508, 1560, 1584, 1620, 1632, 1692, 1740, 1818, 1900, 1920, 1938 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Positions of a(n) in A001043 and A118717: {5, 4}, {7, 6}, {15, 17}, {16, 19}, {17, 21}, {30, 39}, {34, 48}, {37, 53}, {42, 60}, {51, 77}. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 24 is a term because 24 = 11+13 and 24 = 10+14. Alternatively, 24 = A001043(5) = A118717(4), 36 = A001043(7) = A118717(6). MATHEMATICA sp=Select[Range[4, 1000], 2==PrimeOmega[#]&]; Select[Table[sp[[k]]+sp[[k+1]], {k, 100}], #==(p=NextPrime[#/2, -1])+NextPrime[p]&] Module[{nn=2000, sp}, sp=Total/@Partition[Select[Range[nn], PrimeOmega[#]==2&], 2, 1]; Intersection[ sp, Total/@Partition[Prime[Range[nn]], 2, 1]]] (* Harvey P. Dale, Jul 31 2023 *) PROG (PARI) issemi(n)=bigomega(n)==2 nextsp(x)=x=ceil(x); while(!issemi(x), x++); x has(n)=precprime((n-1)/2)+nextprime(n/2)==n list(lim)=my(v=List(), last=4, t); forfactored(n=6, nextsp(lim\2), if(vecsum(n[2][, 2])==2, if(has(t=last+n[1]) && t<=lim, listput(v, t)); last=n[1])); Vec(v) \\ Charles R Greathouse IV, Feb 19 2018 CROSSREFS Intersection of A001043 and A118717. Sequence in context: A347422 A278474 A327946 * A108190 A185489 A303884 Adjacent sequences: A288946 A288947 A288948 * A288950 A288951 A288952 KEYWORD nonn AUTHOR Zak Seidov, Jun 20 2017 STATUS approved

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Last modified August 12 09:11 EDT 2024. Contains 375085 sequences. (Running on oeis4.)