A092146 -id:A092146 - cp's OEIS frontend

A023203 Primes p such that p + 10 is also prime.

3, 7, 13, 19, 31, 37, 43, 61, 73, 79, 97, 103, 127, 139, 157, 163, 181, 223, 229, 241, 271, 283, 307, 337, 349, 373, 379, 409, 421, 433, 439, 457, 499, 547, 577, 607, 631, 643, 673, 691, 709, 733, 751, 787, 811, 829, 853, 877, 919, 937, 967, 1009, 1021, 1039, 1051

Offset: 1

David W. Wilson

A subset of A002476. It appears that this is also a subset of A007645. The first few terms of A007645 that are not in this sequence are {67, 109, 151, 193, 199, 211, 277, 313, 331, 367, 397, 463, 487, 523, 541, 571, 601, 613, ...}. - Alexander Adamchuk, Aug 15 2006

The entries are all in A007645, because they cannot be of the form p = 3*j + 2. If they were, p + 10 = 3*j + 12 would be divisible by 3 and not prime. - R. J. Mathar, Oct 30 2009

Matt C. Anderson, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)
Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
Eric Weisstein's World of Mathematics, Twin Primes

Different from A015916. Cf. A031928, A079033.

Cf. A002476, A007645, A092146.

[n: n in [0..1000] | IsPrime(n) and IsPrime(n+10)]; // Vincenzo Librandi, Nov 20 2010

for p from 1 to 10000 do if isprime(p) and isprime(p+10) then print(p) end if end do # Matt C. Anderson, Aug 26 2022

Select[Prime[Range[200]], PrimeQ[# + 10] &] (* Harvey P. Dale, Dec 14 2011 *)

is(n)=isprime(n)&&isprime(n+10) \\ Charles R Greathouse IV, Jul 01 2013

Revised by N. J. A. Sloane, Jan 29 2013

New name from Michel Marcus, Mar 04 2020

A092216 Primes of the form p + 12 where p is a prime.

Original entry on oeis.org

17, 19, 23, 29, 31, 41, 43, 53, 59, 71, 73, 79, 83, 101, 109, 113, 139, 149, 151, 163, 179, 191, 193, 211, 223, 239, 241, 251, 263, 269, 281, 283, 293, 349, 359, 379, 401, 409, 421, 431, 433, 443, 461, 479, 491, 499, 503, 521, 569, 599, 613, 619, 631, 643, 653

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Apr 02 2004

nonn

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

Cf. A000040, A006512, A046132, A046117, A092402, A092146.

f[n_]:=n+12; lst={};Do[r=Prime[n];p=f[r];If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 04 2009 *)
Select[Prime[Range[5,120]],PrimeQ[#-12]&]  (* Harvey P. Dale, Feb 18 2011 *)

a(n) = 12 + A046133(n). - R. J. Mathar, Jun 21 2010

A140445 List of prime pairs of form p, p + 10.

Original entry on oeis.org

3, 13, 7, 17, 13, 23, 19, 29, 31, 41, 37, 47, 43, 53, 61, 71, 73, 83, 79, 89, 97, 107, 103, 113, 127, 137, 139, 149, 157, 167, 163, 173, 181, 191, 223, 233, 229, 239, 241, 251, 271, 281, 283, 293, 307, 317, 337, 347, 349, 359, 373, 383, 379, 389, 409, 419, 421

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2008

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A023203 (1st bisection), A092146 (2nd bisection).

Cf. prime pairs of the form (p, p+k): A077800 (k=2), A094343 (k=4), A156274 (k=6), A156320 (k=8), this sequence (k=10), A156323 (k=12), A140446 (k=14), A272815 (k=16), A156328 (k=18), A272816 (k=20), A140447 (k=22).

i: 1: for k from 1 to 1200 do if isprim (k) and isprim (k+10) then a [ i ] : = k : a [ i + 1]: = k + 10 : i = i + 2 fi od : seq (a [ n ], n=1..i-1);

Flatten[{#,#+10}&/@Select[Prime[Range[100]],PrimeQ[#+10]&]]  (* Harvey P. Dale, Apr 11 2011 *)

Corrected by D. S. McNeil, Dec 10 2009

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

A140547 Primes p such that neither p - 10 nor p + 10 is prime.

Original entry on oeis.org

2, 5, 11, 59, 67, 101, 109, 131, 151, 179, 193, 197, 199, 211, 227, 257, 263, 269, 277, 311, 313, 331, 353, 367, 397, 401, 461, 463, 479, 487, 491, 503, 521, 523, 541, 563, 569, 571, 593, 599, 601, 613, 619, 647, 659, 661, 677, 727, 739, 757, 769, 773, 809

Offset: 1

Juri-Stepan Gerasimov, Jun 30 2008, Nov 07 2009

Cf. A023203, A092146.

Select[Prime[Range[140]],!PrimeQ[#+10]&&(!PrimeQ[#-10]||#<10)&] (* James C. McMahon, Jul 12 2025 *)

Edited by Charles R Greathouse IV, Mar 25 2010

cp's OEIS Frontend

A023203 Primes p such that p + 10 is also prime.

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A092216 Primes of the form p + 12 where p is a prime.

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A140445 List of prime pairs of form p, p + 10.

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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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PARI

A140547 Primes p such that neither p - 10 nor p + 10 is prime.

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