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.

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A179007 Sum of 3 consecutive composite odd numbers.

Original entry on oeis.org

45, 61, 73, 85, 95, 107, 119, 133, 145, 155, 163, 175, 185, 197, 209, 221, 233, 243, 253, 263, 271, 279, 287, 299, 315, 331, 343, 351, 357, 363, 369, 377, 387, 397, 409, 419, 429, 435, 445, 455, 467, 475, 485, 495, 505, 515, 523, 535, 545, 555, 561, 571, 585, 599
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 07 2011

Keywords

Examples

			9+15+21=45, 15+21+25=61, 21+25+27=73,..

Crossrefs

Cf. A034962, A034965, A082246

Programs

  • Mathematica
    t=Select[Range[2, 200], OddQ[#] && ! PrimeQ[#] &]; Plus @@@ Partition[t, 3, 1]

A179012 Primes that are the sum of three consecutive composite odd numbers.

Original entry on oeis.org

61, 73, 107, 163, 197, 233, 263, 271, 331, 397, 409, 419, 467, 523, 571, 599, 677, 691, 757, 827, 839, 883, 929, 997, 1039, 1051, 1063, 1097, 1123, 1153, 1163, 1171, 1187, 1223, 1231, 1291, 1301, 1367, 1433, 1493, 1523, 1531, 1571, 1619, 1627, 1637, 1667, 1693, 1783
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 07 2011

Keywords

Examples

			15+21+25=61, 21+25+27=73, 33+35+39=107.

Links

Crossrefs

Cf. A034962, A034965, A082246, A179007.

Programs

  • Mathematica
    lst={};Do[If[!PrimeQ[n],s=n;k=1,Continue[]];If[!PrimeQ[n+2],s+=n+2;k=2;q=2,If[!PrimeQ[n+4],s+=n+4;k=2;q=4,If[!PrimeQ[n+6],s+=n+6;k=2;q=6]]];If[!PrimeQ[n+q+2],s+=n+q+2;k=3;q+=2,If[!PrimeQ[n+q+4],s+=n+q+4;k=3;q+=4,If[!PrimeQ[n+q+6],s+=n+q+6;k=3;q+=6]]];If[PrimeQ[s],AppendTo[lst,s]],{n,9,6!,2}];lst
nn=1001;With[{compodd=Complement[Range[9,nn,2],Prime[Range[ PrimePi[ nn]]]]}, Select[ Total/@ Partition[compodd,3,1],PrimeQ]] (* Harvey P. Dale, Dec 09 2012 *)

A125270 Coefficient of x^2 in polynomial whose zeros are 5 consecutive primes starting with the n-th prime.

Original entry on oeis.org

1358, 3954, 10478, 22210, 43490, 78014, 129530, 206650, 324350, 466270, 621466, 853742, 1132130, 1436690, 1870850, 2388050, 2886370, 3440410, 4133410, 4904906, 5926654, 7195670, 8425430, 9792950, 11040910, 12098990, 13917898, 16097810
Offset: 1

Views

Author

Artur Jasinski, Jan 16 2007

Keywords

Comments

Sums of all distinct products of 3 out of 5 consecutive primes, starting with the n-th prime; value of 3rd elementary symmetric function on the 5 consecutive primes.

Crossrefs

Cf. A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127338, A127339, A127340, A127341, A127342, A127343, A127345, A127346, A127347, A127348, A127349, A127351, A037171, A034962, A034965, A082246, A082251, A070934, A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127489.

Programs

  • Mathematica
    a = {}; Do[AppendTo[a, (Prime[x] Prime[x + 1] Prime[x + 2] + Prime[x] Prime[x + 1] Prime[x + 3] + Prime[x] Prime[x + 1] Prime[x + 4] + Prime[x] Prime[x + 2] Prime[x + 3] + Prime[x] Prime[x + 2] Prime[x + 4] + Prime[x] Prime[x + 3] Prime[x + 4] + Prime[x + 1] Prime[x + 2] Prime[x + 3] + Prime[x + 1] Prime[x + 2] Prime[x + 4] + Prime[x + 1] Prime[x + 3] Prime[x + 4] + Prime[x + 2] Prime[x + 3] Prime[x + 4])], {x, 1, 100}]; a
fcp[{p_,q_,r_,s_,t_}]:=p*q(r+s+t)+(p+q)r(s+t)+(p+q+r)s*t; fcp/@Partition[ Prime[ Range[40]],5,1] (* Harvey P. Dale, Sep 05 2014 *)

Formula

Let p = Prime(n), q = Prime(n+1), r = Prime(n+2), s = Prime(n+3) and t = Prime(n+4). Then a(n) = p q (r+s+t) + (p + q) r (s + t) + (p + q + r) s t.

Extensions

Edited and corrected by Franklin T. Adams-Watters, Jan 23 2007

A341338 a(n) is the smallest prime that is simultaneously the sum of 2n-1, 2n+1 and 2n+3 consecutive primes.

Original entry on oeis.org

83, 311, 55813, 437357, 1219789, 8472193, 9496853, 6484103, 2166953, 37296143, 12671599, 13432571, 14968909, 145616561, 732092831, 220872569, 1381099933, 93482633, 4142423, 87030017, 3193060007, 736535783, 6390999871, 280886077, 464341303, 268231657, 686836817, 9000046663
Offset: 1

Views

Author

Zak Seidov, Apr 25 2021

Keywords

Examples

			For n = 1: 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23, and 83 is the smallest prime that is the sum of 1, 3 and 5 consecutive primes, so a(1) = 83.

Crossrefs

Cf. A034962, A034965, A082246, A082251, A127340, A127341, A161612.

Programs

  • Mathematica
    Array[(k=1;
While[(i=Select[Intersection@@((Total/@Subsequences[Prime@Range@Prime[k++],{#}])&/@{2#-1,2#+1,2#+3}),PrimeQ])=={}];First@i)&,4] (* Giorgos Kalogeropoulos, Apr 26 2021 *)
Previous Showing 11-14 of 14 results.

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