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!)
A055469 Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers). 20
2, 7, 11, 29, 37, 67, 79, 137, 191, 211, 277, 379, 631, 821, 947, 991, 1129, 1327, 1597, 1831, 2017, 2081, 2347, 2557, 2851, 2927, 3571, 3917, 4561, 4657, 4951, 5051, 5779, 6217, 6329, 8647, 8779, 9181, 9871, 11027, 12721, 13367, 14029, 14197, 14879 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also primes of the form (n^2 + 7)/8. - Ray Chandler, Oct 08 2005
q=2 and q=5 are the only primes values such that q+1 is a triangular number because 8q+9 is a square for 2 and 5 only. - Benoit Cloitre, Apr 05 2002
n such that A000010(n) = A000217(k). - Giovanni Teofilatto, Jan 29 2010
It is conjectured that this sequence is infinite. - Daniel Forgues, Apr 21 2015
LINKS
FORMULA
a(n) = A000124(A067186(n)) = (A110873(n) + 7)/8. - Ray Chandler, Oct 08 2005
MATHEMATICA
Select[Table[(n^2 + 7)/8, {n, 400}], PrimeQ] (* Ray Chandler, Oct 08 2005 *)
Select[Accumulate[Range[400]]+1, PrimeQ] (* Harvey P. Dale, May 14 2022 *)
PROG
(PARI) forprime(p=2, 10^5, if ( issquare(8*p-7), print1(p, ", "))) \\ Joerg Arndt, Jul 14 2012
(PARI) list(lim)=my(v=List(), p); forstep(s=3, sqrtint(lim\1*8-7), 2, if(isprime(p=(s^2+7)/8), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, May 05 2020
CROSSREFS
Sequence in context: A309471 A073602 A057025 * A361151 A327552 A336342
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jun 27 2000
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 June 17 13:47 EDT 2024. Contains 373445 sequences. (Running on oeis4.)