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 1-6 of 6 results.

A164132 Primes which are an eighth of the sum of two consecutive primes.

Original entry on oeis.org

3, 19, 59, 89, 109, 149, 151, 317, 331, 359, 389, 401, 439, 571, 599, 829, 941, 953, 1019, 1153, 1249, 1279, 1319, 1373, 1381, 1451, 1657, 1669, 1733, 1741, 1867, 1871, 1973, 2131, 2161, 2179, 2251, 2459, 2819, 3119, 3539, 3659, 3967, 4001, 4099, 4231, 4261
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 11 2009

Keywords

Comments

Primes of the form A001043(k)/8.

Examples

			19 is there because it is prime and 19=(73+79)/8.

Links

Crossrefs

Cf. A000040, A118134, A163487.

Programs

  • Maple
    p:= 2: R:= NULL: count:= 0:
while count < 100 do
 q:= p; p:= nextprime(p);
 v:= (q+p)/8;
 if v::integer and isprime(v) then
   R:= R,v; count:= count+1;
 fi;
od:
R; # Robert Israel, Dec 08 2024
  • Mathematica
    Select[Total[#]/8&/@Partition[Prime[Range[2500]],2,1],PrimeQ]  (* Harvey P. Dale, Apr 22 2011 *)

Extensions

Extended by R. J. Mathar, Aug 27 2009

A164134 Primes p such that 12*p is the sum of two consecutive primes.

Original entry on oeis.org

2, 3, 5, 7, 17, 23, 31, 41, 47, 71, 97, 103, 107, 137, 139, 193, 283, 313, 337, 347, 349, 373, 397, 421, 443, 467, 487, 491, 577, 587, 593, 619, 631, 643, 653, 673, 691, 701, 773, 787, 811, 827, 907, 991, 1021, 1033, 1051, 1093, 1117, 1217, 1249, 1259, 1289
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 11 2009

Keywords

Examples

			p=17 is there because it is prime and 12*17=101+103 = A001043(26) .

Links

Crossrefs

Cf. A000040, A001043, A118134, A163487.

Programs

  • Mathematica
    Select[ListConvolve[{1,1},Prime[Range[2000]]]/12,PrimeQ] (* Paolo Xausa, Nov 03 2023 *)

Extensions

233 replaced by 283 and extended by R. J. Mathar, Aug 21 2009

A164133 Primes p such that 4*p and 6*p are each the sum of two consecutive primes.

Original entry on oeis.org

2, 3, 13, 43, 127, 167, 613, 647, 1033, 1483, 1543, 2297, 2927, 3701, 3823, 4463, 5101, 5417, 5657, 6133, 8081, 9227, 11273, 11833, 12511, 13291, 13873, 17627, 19853, 20011, 21313, 21727, 22193, 23041, 23059, 23081, 23159, 24443, 26347, 26947, 27407, 27527
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 11 2009

Keywords

Examples

			p=13 is in the sequence because 4*13 = 52 = A001043(9) and 6*13 = 78 = A001043(12) are both in A001043.

Links

Crossrefs

Cf. A000040, A118134, A163487.

Programs

  • Maple
    P:= select(isprime, [2,seq(i,i=3..10^6)]):
PS:= P[1..-2] + P[2..-1]:
convert(P,set) intersect convert(1/4 * PS, set) intersect convert(1/6*PS,set); # Robert Israel, Dec 08 2024
  • Mathematica
    stcpQ[n_]:=Module[{a=4n,b=6n},a==NextPrime[a/2]+NextPrime[a/2,-1]&&b== NextPrime[b/2]+NextPrime[b/2,-1]]; Select[Prime[Range[3100]],stcpQ] (* Harvey P. Dale, May 01 2019 *)

Formula

A163487 INTERSECT A118134.

Extensions

Extended by R. J. Mathar, Aug 27 2009

A289270 Primes p such that 10*p is the sum of two consecutive primes.

Original entry on oeis.org

3, 41, 103, 293, 359, 379, 421, 653, 701, 733, 821, 883, 907, 911, 937, 1009, 1237, 1423, 1567, 1627, 1637, 1931, 1973, 2017, 2129, 2203, 2281, 2417, 2459, 2477, 2647, 2879, 3209, 3271, 3347, 3413, 3539, 3593, 3659
Offset: 1

Views

Author

Zak Seidov, Jun 30 2017

Keywords

Examples

			10*3 = 30 = prime(6) + prime(7) = 13+17;
10*41 = 410 = prime(46) + prime(47) = 199+211.

Links

Crossrefs

Primes p such that m*p is the sum of two consecutive primes: A118134 (m=4), A163487 (m=6), A164132 (m=8), this sequence (m=10), A164134 (m=12).

Programs

  • Mathematica
    Select[Map[Total, Partition[Prime@ Range@ 2200, 2, 1]]/10, PrimeQ] (* Michael De Vlieger, Jun 30 2017 *)
  • PARI
    is(n)=isprime(n) && precprime(5*n)+nextprime(5*n)==10*n \\ Charles R Greathouse IV, Jul 02 2017

A339775 Primes p such that (p+nextprime(p))/6 is prime and 6*p is the sum of two consecutive primes.

Original entry on oeis.org

5, 7, 13, 37, 127, 389, 719, 937, 3089, 7669, 9199, 12211, 17099, 17519, 18919, 19259, 19273, 19853, 20063, 21379, 22453, 22643, 23059, 23143, 23173, 23753, 24113, 24329, 25339, 25873, 31387, 31667, 32803, 33203, 34057, 34183, 36629, 37253, 37831, 37967, 38557, 39293, 40429, 41039, 42743, 48163
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Dec 16 2020

Keywords

Examples

			a(3) = 13 is a term because 13 is prime, the next prime is 17, (13+17)/6 = 5 is prime, and 6*13 = 78 = 37 + 41 is the sum of consecutive primes.

Links

Crossrefs

Intersection of A163487 and A288632.

Programs

  • Maple
    filter:= proc(p) local q;
  if not isprime(p) then return false fi;
  q:= prevprime(3*p);
  if q + nextprime(q) <> 6*p then return false fi;
  q:= (p+nextprime(p))/6;
  q::integer and isprime(q)
end proc:
select(filter, [seq(i,i=3..10^5,2)]);

A163488 Primes p such that 5*p is a sum of 3 consecutive primes.

Original entry on oeis.org

2, 3, 47, 79, 113, 197, 227, 257, 263, 317, 347, 383, 431, 443, 491, 499, 541, 557, 617, 757, 811, 887, 929, 977, 1021, 1087, 1093, 1129, 1231, 1237, 1433, 1511, 2111, 2129, 2213, 2347, 2543, 2551, 2609, 2657, 2671, 2803, 2837, 2999, 3011, 3049, 3119, 3187
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 28 2009

Keywords

Comments

Primes of the form A034961(k)/5, associated with k=1, 2, 21, 31, 42, 66,... - R. J. Mathar, Aug 02 2009

Examples

			p=2 is in the sequence because 2*5=10=2+3+5.
p=3 is in the sequence because 3*5=15=3+5+7.

Crossrefs

Cf. A006562, A118134, A163487.

Programs

  • Mathematica
    lst={};Do[If[PrimeQ[p=(Prime[n]+Prime[n+1]+Prime[n+2])/5],AppendTo[lst, p]],{n,7!}];lst
cp3Q[n_]:=Module[{mid=Floor[PrimePi[(5n)/3]],tst},tst=Total/@ Partition[ Prime[ Range[mid-10,mid+10]],3,1];MemberQ[tst,5n]]; Select[ Prime[ Range[ 500]],cp3Q]//Quiet (* Harvey P. Dale, Jan 02 2018 *)

Extensions

Entries checked by R. J. Mathar, Aug 02 2009
Showing 1-6 of 6 results.

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