The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298464 The first of two consecutive primes the sum of which is equal to the sum of two consecutive pentagonal numbers. 5
79, 3643, 10909, 37123, 56053, 70849, 78889, 125551, 178877, 209063, 258743, 330409, 350411, 395261, 439559, 469279, 479387, 499969, 620813, 663997, 754723, 828811, 878597, 901709, 1026709, 1087147, 1170397, 1202429, 1213189, 1234873, 1340477, 1510013 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
79 is in the sequence because 79+83 (consecutive primes) = 162 = 70+92 (consecutive pentagonal numbers).
MATHEMATICA
Block[{s = Total /@ Partition[PolygonalNumber[5, Range[10^3]], 2, 1], t}, t = Partition[Prime@ Range@ PrimePi[2 Last[s]], 2, 1]; Select[t, MemberQ[s, Total@ #] &][[All, 1]]] (* Michael De Vlieger, Jan 21 2018 *)
PROG
(PARI) L=List(); forprime(p=2, 1600000, q=nextprime(p+1); t=p+q; if(issquare(12*t-8, &sq) && (sq-2)%6==0, u=(sq-2)\6; listput(L, p))); Vec(L)
(Python)
from __future__ import division
from sympy import prevprime, nextprime
A298464_list, n, m = [], 1 , 6
while len(A298464_list) < 10000:
k = prevprime(m//2)
if k + nextprime(k) == m:
A298464_list.append(k)
n += 1
m += 6*n-1 # Chai Wah Wu, Jan 20 2018
CROSSREFS
Sequence in context: A205496 A017795 A017742 * A078114 A038531 A032910
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 19 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 19:57 EDT 2024. Contains 372952 sequences. (Running on oeis4.)