A092216 -id:A092216 - cp's OEIS frontend

A137796 Prime numbers p such that p + 12 and p - 12 are primes.

17, 19, 29, 31, 41, 59, 71, 101, 139, 151, 179, 211, 239, 251, 269, 281, 409, 421, 431, 479, 491, 619, 631, 739, 809, 941, 1009, 1021, 1051, 1289, 1291, 1439, 1459, 1471, 1499, 1511, 1571, 1609, 1709, 1721, 1789, 1889, 1901, 1999, 2099, 2141, 2281, 2411

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 28 2008

nonn

			17 + 12 = 29 (a prime), 17 - 12 = 5 (a prime);
19 + 12 = 31 (a prime), 19 - 12 = 7 (a prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A092216, A046133. Note that this is different from A137873.

isA092216 := proc(n) RETURN(isprime(n) and isprime(n-12) ) ; end: isA046133 := proc(n) RETURN(isprime(n) and isprime(n+12) ) ; end: isA137796 := proc(n) RETURN(isA092216(n) and isA046133(n)) ; end: for i from 1 to 400 do if isA137796(ithprime(i)) then printf("%d,",ithprime(i)) ; fi ; od: # R. J. Mathar, May 03 2008

a=12; Select[Table[Prime[n],{n,10^3}], PrimeQ[ #-a] && PrimeQ[ #+a] &]

lista(nn) = forprime(p=2, nn, if (isprime(p-12) && isprime(p+12), print1(p, ", "))); \\ Michel Marcus, Oct 04 2015

A092216 INTERSECT A046133. - R. J. Mathar, May 03 2008

Corrected and extended by R. J. Mathar, May 03 2008

A156323 List of prime pairs of the form (p, p+12).

Original entry on oeis.org

5, 17, 7, 19, 11, 23, 17, 29, 19, 31, 29, 41, 31, 43, 41, 53, 47, 59, 59, 71, 61, 73, 67, 79, 71, 83, 89, 101, 97, 109, 101, 113, 127, 139, 137, 149, 139, 151, 151, 163, 167, 179, 179, 191, 181, 193, 199, 211, 211, 223, 227, 239, 229, 241, 239, 251, 251, 263, 257

Offset: 1

Vincenzo Librandi, Feb 08 2009

			For p=5, 5+12=17, (5,17); p=59, 59+12=71, (59,71)

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A046133, A092216.

Flatten[Select[{#,#+12}&/@Prime[Range[100]], PrimeQ[Last[#]]&]]  (* Harvey P. Dale, Mar 23 2011 *)

A206768 a(n) = smallest number k such that sigma(k-n) = sigma(k) - n, with k > n+1.

Original entry on oeis.org

3, 5, 5, 7, 7, 11, 81, 11, 11, 13, 13, 17, 4431, 17, 17, 19, 19, 23, 25, 23, 23, 29

Offset: 1

Paolo P. Lava, Jan 10 2013

This sequence begins
3, 5, 5, 7, 7, 11, 81, 11, 11, 13, 13, 17, 4431, 17, 17, 19, 19, 23, 25, 23, 23, 29, ?, 29, ?, 29, 29, 31, 31, 37, ?, 37, 51, 37, 37, 41, 81, 41, 41, 43, 43, 47, ?, 47, 47, 53, ?, 53, 3364, 53, 53, 59, ?, 59, ?, 59, 59, 61, 61, 67, ?, 67, ?, 67, 67, 71, ?, 71, 71, 73, 73, 79, 91, 79, ?, 79, 79, 83, ?, 83, 83, 89, ?, 89, ?, 89, 89, 101, ?, 97, ?, 97, 125, 97, 97, 101, ?, 101, 101, 103, 103, 107... where the other missing terms (designated by "?") are > 10^6, if they exist.
For a given n, n being even, among the integers k satisfying the property sigma(k-n) = sigma(k)-n, we will find prime numbers p, such that p and p-n are primes. This is because in that case sigma(p-n) = (p-n)+1 = (p+1)-n = sigma(p)-n. For instance, when n is even, for n=2 to 14, a(n) is the first term of A006512, A046132, A046117, A092402, A092146, A092216, A098933. If we restrict to composite numbers, then see A084293. - Michel Marcus, Feb 16 2013
For the missing terms mentioned in first comment, a(n) is > 10^7. - Michel Marcus, Sep 21 2013

			a(13) = 4431 because 4431 is the minimum number for which sigma(4431-13) = sigma(4418)= 6771 and sigma(4431) - 13 = 6784 -13 = 6771.
a(19) = 25 because 25 is the minimum number for which sigma(25-19) = sigma(6) = 12 and sigma(25) - 19 = 31 -19 = 12.

Cf. A015886.

A206768:=proc(q)
local k,n;
for n from 1 to q do
  for k from n+1 to q do
  if sigma(-n+k)=sigma(k)-n then print(k); break; fi;
od; od; end:
A206768(1000000000);

A098933 Primes of the form p+14, where p is a prime.

Original entry on oeis.org

17, 19, 31, 37, 43, 61, 67, 73, 97, 103, 127, 151, 163, 181, 193, 211, 241, 271, 277, 283, 307, 331, 367, 373, 397, 433, 457, 463, 523, 571, 577, 601, 607, 613, 631, 661, 673, 691, 733, 757, 787, 811, 823, 853, 877, 967, 991, 997, 1033, 1063, 1117, 1123, 1201

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Oct 20 2004

Cf. A000040 A006512 A067829 A094743 A046132 A067830 A046117 A067831 A092402 A092146 A092216.

isok(n) = isprime(n) && isprime(n - 14) \\ Michel Marcus, Jul 17 2013

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A137796 Prime numbers p such that p + 12 and p - 12 are primes.

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A156323 List of prime pairs of the form (p, p+12).

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A206768 a(n) = smallest number k such that sigma(k-n) = sigma(k) - n, with k > n+1.

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A098933 Primes of the form p+14, where p is a prime.

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