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.

A086522 Primes arising as the arithmetic mean of a pair of successive terms of A086519.

Original entry on oeis.org

5, 13, 31, 37, 67, 127, 109, 73, 103, 163, 181, 151, 181, 277, 271, 241, 277, 331, 373, 337, 373, 463, 547, 577, 523, 571, 607, 547, 571, 541, 547, 661, 709, 733, 811, 853, 787, 769, 823, 883, 859, 937, 991, 1021, 1087, 1009, 1069, 1129, 1039, 1231, 1381
Offset: 1

Views

Author

Amarnath Murthy, Jul 30 2003

Keywords

Comments

Second term onwards every prime == 1 (mod 6).
Conjecture: every prime of the type 6k+1 is a member. Comment from Vim Wenders, May 27 2008: The conjecture is worng. For example 19 is missing..

Crossrefs

Cf. A086519.

Formula

a(n) = (A086519(n)+A086519(n+1))/2. - David Wasserman, Mar 11 2005

Extensions

Corrected and extended by David Wasserman, Mar 11 2005

A086523 Beginning with 5, distinct odd primes such that the arithmetic mean of every pair of successive terms is prime.

Original entry on oeis.org

5, 17, 29, 53, 41, 101, 113, 149, 197, 257, 269, 293, 401, 461, 521, 593, 641, 653, 701, 821, 857, 1049, 1277, 1289, 1433, 1553, 1613, 1721, 1901, 1913, 1949, 1997, 2081, 2141, 2273, 2393, 2441, 2477, 2609, 2633, 2693, 2729, 2753, 2801, 2837, 2957, 2969
Offset: 1

Views

Author

Amarnath Murthy, Jul 30 2003

Keywords

Comments

Every term == -1 (mod 6).
Conjecture: every prime of the form 6k-1 is a member. Comment from Vim Wenders, May 27 2008: The conjecture is wrong. For example 11 and 23 are missing.

Crossrefs

Cf. A086519, A086522, A086524.

Extensions

More terms from Ray G. Opao, Jan 24 2005

A086524 Primes arising as the arithmetic mean of a pair of successive terms of A086523.

Original entry on oeis.org

11, 23, 41, 47, 71, 107, 131, 173, 227, 263, 281, 347, 431, 491, 557, 617, 647, 677, 761, 839, 953, 1163, 1283, 1361, 1493, 1583, 1667, 1811, 1907, 1931, 1973, 2039, 2111, 2207, 2333, 2417, 2459, 2543, 2621, 2663, 2711, 2741, 2777, 2819, 2897, 2963, 3089
Offset: 1

Views

Author

Amarnath Murthy, Jul 30 2003

Keywords

Comments

Every term == -1 (mod 6). Conjecture: every prime of the form 6k-1 is a member.

Crossrefs

Cf. A086519, A086522, A086523.

Extensions

More terms from Ray G. Opao, Jan 24 2005

A164622 Primes p such that p*floor(p/2) - 4 and p*floor(p/2) + 4 are prime numbers.

Original entry on oeis.org

151, 463, 571, 631, 643, 991, 1063, 1171, 1831, 2083, 2311, 4951, 5023, 6211, 6703, 6763, 7723, 7951, 9043, 11383, 12163, 12391, 13183, 14851, 15031, 17431, 19231, 19543, 20143, 22051, 23143, 25951, 26371, 27283, 28351, 29131, 30643, 32803
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 17 2009

Keywords

Comments

151*75-4=11321 (prime), 151*75+4=11329 (prime), ..

Crossrefs

Subsequence of A068229. Cf. A008846, A020882, A068229, A086519, A158708, A164620, A164621

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p*Floor[p/2]-4]&&PrimeQ[p*Floor[p/2]+4],AppendTo[lst,p]],{n,8!}];lst

Extensions

Edited by Charles R Greathouse IV, Nov 02 2009

A164623 Primes p such that p*(p-1)/2-5 and p*(p-1)/2+5 are also prime numbers.

Original entry on oeis.org

13, 157, 673, 1069, 1117, 1153, 1213, 1597, 2029, 2089, 2437, 2713, 2833, 3613, 4057, 4909, 5653, 6337, 6529, 7549, 7993, 8053, 9613, 10789, 11497, 11689, 12073, 12373, 13309, 13669, 13789, 14173, 15289, 15937, 16249, 18097, 18637, 19249, 19993
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 17 2009

Keywords

Comments

Primes A000040(k) such that A008837(k)+-5 are also prime numbers.

Examples

			13 is in the sequence because 13*6-5=73 and 13*6+5=83 are both prime.

Links

Crossrefs

Cf. A008846, A020882, A068228, A068229, A082539, A086519, A107159, A158708, A139494, A164620, A164621, A164622, A023203.

Programs

  • Mathematica
    Select[Prime[Range[2300]], PrimeQ[# (# - 1)/2 - 5] && PrimeQ[# (# - 1)/2 + 5] &]
  • PARI
    forprime(p=2,10^6,my(b=binomial(p,2));if(isprime(b-5)&isprime(b+5),print1(p,", "))); /* Joerg Arndt, Apr 10 2013 */

Extensions

Edited by R. J. Mathar, Aug 20 2009
Mathematica code adapted to the definition by Bruno Berselli, Apr 10 2013

A217606 a(n) is the least unused prime greater than 3 such that (a(n) + a(n-1))/2 is prime, with a(0)=13.

Original entry on oeis.org

13, 61, 73, 181, 37, 97, 109, 193, 229, 157, 241, 313, 349, 277, 337, 397, 421, 373, 541, 433, 409, 457, 757, 661, 577, 709, 613, 601, 853, 769, 733, 1021, 997, 877, 829, 673, 1033, 1009, 1069, 1117, 1129, 937, 1201, 1297, 1549, 1093, 1153, 1249, 1213, 1381
Offset: 0

Views

Author

Pedja Terzic, Oct 08 2012

Keywords

Comments

Conjecture: every prime of the form 12k+1 is a member.

Crossrefs

Cf. A086519.

Programs

  • Maple
    a:=5:
l:=13:
L:=[l]:
while l < 3400 do
if isprime((l+a)/2) then
if not(a in L) then
if not a mod 12 = 1 then
print(a);
break;
end if;
L:=[op(L),a]:
l:=a:
a:=5:
else
a:=nextprime(a):
end if;
else
a:=nextprime(a):
end if;
end do;
L;
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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