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.

A132811 Arithmetic mean of the n primes starting at A132809(n), summed in A132810(n).

Original entry on oeis.org

4, 5, 9, 79, 12, 17, 30, 261, 30, 49, 23, 71, 51, 29, 31, 37, 39, 125, 56, 95, 52, 173, 133, 157, 113, 353, 70, 347, 89, 111, 139, 179, 187, 281, 124, 137, 95, 347, 100, 153, 105, 491, 273, 185, 177, 377, 199, 599, 1032, 149, 274, 277, 200, 485, 251, 155, 315, 713
Offset: 2

Views

Author

Enoch Haga, Sep 01 2007

Keywords

Examples

			a(5)=79, which is the arithmetic mean 395/5 of the n=5 primes 71=A132809(n), 73, 79, 83 and 89, which add to A132810(n)=395.

Crossrefs

Cf. A132809, A132810.

Formula

a(n)=A132810(n)/n. - R. J. Mathar, Nov 27 2007

Extensions

Edited by R. J. Mathar, Nov 27 2007

A132809 First prime in a sequence of n consecutive odd primes with integral arithmetic mean.

Original entry on oeis.org

3, 3, 5, 71, 5, 7, 17, 239, 13, 29, 5, 43, 23, 5, 5, 7, 7, 79, 17, 47, 11, 109, 73, 97, 53, 271, 13, 263, 23, 41, 61, 97, 101, 181, 41, 47, 13, 233, 13, 53, 13, 359, 151, 71, 61, 239, 73, 443, 859, 29, 131, 131, 61, 313, 101, 19, 151, 521, 3, 571, 31, 7, 79, 109, 97, 53, 53
Offset: 2

Views

Author

Enoch Haga, Sep 01 2007

Keywords

Comments

See A054892 for another version.

Examples

			For n=2 we add prime(2)+prime(3)=3+5=8 which is already a multiple of n=2, so we add the first of the primes, 3, at a(n=2).
For n=5 we test 3+5+7+11+13=39 against being a multiple of n=5, then 5+7+11+13+17=53, then 7+11+13+17+19=67 etc. and find that 71+73+79+83+89=395 is a multiple. We place the smallest member in this sequence of 5 primes, 71, at a(n=5).

Crossrefs

Cf. A132810-A132811, A054892.

Programs

  • Maple
    A132809 := proc(n) local i,j ; for i from 2 do if add( ithprime(i+j),j=0..n-1) mod n = 0 then RETURN(ithprime(i)) ; fi ; od: end: seq(A132809(n),n=2..80) ; # R. J. Mathar, Nov 27 2007

Formula

a(n) = {min (prime(k)): sum_{i=0..n-1} prime(k+i) = 0 mod n, k>1 }. - R. J. Mathar, Nov 27 2007

Extensions

Edited by R. J. Mathar, Nov 27 2007

A194267 Smallest sum of three distinct primes of the form n*k+1.

Original entry on oeis.org

10, 15, 39, 35, 83, 39, 143, 131, 129, 83, 179, 111, 263, 143, 243, 227, 479, 129, 839, 203, 381, 179, 463, 363, 503, 263, 543, 339, 641, 243, 1367, 547, 597, 479, 563, 219, 965, 839, 549, 563, 1643, 381, 1551, 839, 993, 463, 1883, 531, 1571, 503, 819, 523
Offset: 1

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Examples

			a(1) = 2+3+5 = 10.
a(2) = 3+5+7 = 15.
a(3) = 7+13+19 = 39.
a(4) = 5+13+17 = 35.
a(5) = 11+31+41 = 83.
a(6) = 7+13+19 = 39.

Links

Crossrefs

Cf. A077318, A132810, A193873, A194266.

Programs

  • Mathematica
    Table[ps = Select[Table[n*k + 1, {k, 100}], PrimeQ, 3]; If[Length[ps] == 3, Total[ps], 0], {n, 100}] (* T. D. Noe, Oct 21 2011 *)

A194266 Smallest sum of two distinct primes of the form n*k+1.

Original entry on oeis.org

5, 8, 20, 18, 42, 20, 72, 58, 56, 42, 90, 50, 132, 72, 92, 114, 240, 56, 420, 102, 170, 90, 186, 170, 252, 132, 272, 142, 292, 92, 684, 290, 266, 240, 282, 110, 372, 420, 236, 282, 822, 170, 604, 442, 452, 186, 942, 290, 688, 252, 410, 210, 850, 272, 992
Offset: 1

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Examples

			a(1) = 2+3 = 5
a(2) = 3+5 = 8
a(3) = 7+13 = 20
a(4) = 5+13 = 18
a(5) = 11+31 = 42
a(6) = 7+13 = 20

Crossrefs

Cf. A077318, A132810, A194265, A194267.

Programs

  • Mathematica
    Table[ps = Select[Table[n*k + 1, {k, 100}], PrimeQ, 2]; If[Length[ps] == 2, Total[ps], 0], {n, 100}] (* T. D. Noe, Oct 21 2011 *)
Showing 1-4 of 4 results.

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