A197421
Primes of the form Sum_{k=1..n} prime(k)*prime(k+1).
Original entry on oeis.org
44839, 60859, 130411, 204749, 303767, 902971, 1027969, 1471633, 2514257, 3658769, 6908719, 7415743, 21966317, 28168523, 32413109, 37049567, 44034163, 47856331, 373881787, 425445073, 443609813, 564963589, 732111109, 758871401, 857997893, 995046653, 2489902577
Offset: 1
For n = 22, a(1) = 44839 = 2*3 + 3*5 + 5*7 + ....+ 79*83 where 79 = prime(22) and 83 = prime(23).
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p:=0:for n from 1 to 600 do:p:=p+ithprime(n)*ithprime(n+1): if type(p,prime)=true then printf(`%d, `,p): else fi:od:
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Select[Table[Sum[Prime[k] Prime[k + 1], {k, n}], {n, 400}], PrimeQ] (* Alonso del Arte, Oct 14 2011 *)
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v=List();t=0;p=2;forprime(q=3,1e4,if(isprime(t+=p*q),listput(v,t));p=q);Vec(v) \\ Charles R Greathouse IV, Oct 14 2011
Incorrect a(2243) and beyond removed from b-file by
Andrew Howroyd, Feb 27 2018
A138323
a(n) = Sum_{k = 1..n} prime(k)^prime(k + 1).
Original entry on oeis.org
8, 251, 78376, 1977405119, 34524689549050, 8650450444070886983, 239081086135595395734136, 257829867026393862843621801395
Offset: 1
2^3=8
2^3+3^5=8+243=251
2^3+3^5+5^7=8+243+78125=78376
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P3[n_] := Sum[Prime[i]^Prime[i + 1], {i, 1, n}]; Table[P3[n], {n, 1, 8}]
Accumulate[#[[1]]^#[[2]]&/@Partition[Prime[Range[10]],2,1]] (* Harvey P. Dale, Jan 18 2025 *)
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a(n) = sum(k=1, n, prime(k)^prime(k+1)); \\ Michel Marcus, Jan 25 2016
A197614
a(n) is the smallest prime of the form Sum_{j=1..k} prime(j)*prime(j+1)*...*prime(j+n).
Original entry on oeis.org
44839, 82193, 630859553, 2525696897, 1910131806019, 14899669504506112147, 60135213227903643780817, 4812219756324961, 341826385983784841, 3490785573251518581776138393, 1025219842099467656125852928369, 14472211420055197111499933838371
Offset: 1
For n=1, k=22 gives the smallest prime of the form Sum_{j=1..k} prime(j)*prime(j+1) = 44839 = 2*3 + 3*5 + 5*7 + ... + 79*83 where 79 = prime(22) and 83 = prime(23).
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for n from 1 to 20 do:i:=0:p:=0:for j from 1 to 1000 while(i=0) do: uu:=1:for k from 0 to n do: uu:=uu*ithprime(j+k):od:p:=p+uu:if type(p,prime)=true then i:=1: printf(`%d, `,p):else fi:od:od:
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a(n) = my(k=1, p); while (!isprime(p=sum(j=1, k, prod(i=0, n, prime(j+i)))), k++); p; \\ Michel Marcus, Feb 21 2023
A268062
a(n) = Sum_{k=1..n} prime(k+1)^prime(k).
Original entry on oeis.org
9, 134, 16941, 19504112, 1792179898149, 9906370212804086, 5480396764155014990025, 74620951324354865576898512, 4316720792370367095095683949638501, 17761887757410618772194137156551786713472772, 4113915065494528452775640793448453170290434881585
Offset: 1
a(3) = 3^2+5^3+7^5 = 16941.
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[&+[NthPrime(k+1)^NthPrime(k): k in [1..n]]: n in [1..12]]; // Vincenzo Librandi, Jan 26 2016
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Table[Sum[Prime[k+1]^Prime[k], {k, 1, n}], {n, 1, 12}] (* Vaclav Kotesovec, Jan 25 2016 *)
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a(n) = sum(k=1, n, prime(k+1)^prime(k)); \\ Michel Marcus, Jan 26 2016
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[sum(nth_prime(i+1)^nth_prime(i) for i in [1..n]) for n in [1..15]] # Tom Edgar, Jan 25 2016
Showing 1-4 of 4 results.
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