cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Michel Lagneau, Oct 14 2011

Keywords

Comments

The corresponding values of n are 22, 24, 30, 34, 38, 52, 54, 60, 70, 78, 94, 96, ....

Examples

			For n = 22, a(1) = 44839 = 2*3 + 3*5 + 5*7 + ....+ 79*83 where 79 = prime(22) and 83 = prime(23).
		

Crossrefs

Primes in A074745.
Cf. A013918.

Programs

  • Maple
    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:
  • Mathematica
    Select[Table[Sum[Prime[k] Prime[k + 1], {k, n}], {n, 400}], PrimeQ] (* Alonso del Arte, Oct 14 2011 *)
  • PARI
    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

Extensions

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

Views

Author

Keywords

Examples

			2^3=8
2^3+3^5=8+243=251
2^3+3^5+5^7=8+243+78125=78376
		

Crossrefs

Programs

  • Mathematica
    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 *)
  • PARI
    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

Views

Author

Michel Lagneau, Oct 16 2011

Keywords

Comments

Generalization of A197421.

Examples

			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).
		

Crossrefs

Programs

  • Maple
    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:
  • PARI
    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

Views

Author

Emre APARI, Jan 25 2016

Keywords

Comments

Partial sums of A078422. - Michel Marcus, Jan 26 2016

Examples

			a(3) = 3^2+5^3+7^5 = 16941.
		

Crossrefs

Programs

  • Magma
    [&+[NthPrime(k+1)^NthPrime(k): k in [1..n]]: n in [1..12]]; // Vincenzo Librandi, Jan 26 2016
    
  • Mathematica
    Table[Sum[Prime[k+1]^Prime[k], {k, 1, n}], {n, 1, 12}] (* Vaclav Kotesovec, Jan 25 2016 *)
  • PARI
    a(n) = sum(k=1, n, prime(k+1)^prime(k)); \\ Michel Marcus, Jan 26 2016
  • Sage
    [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.