A031929 -id:A031929 - cp's OEIS frontend

A134100 Primes p > 3 such that neither p-2 nor p-4 are prime.

29, 37, 53, 59, 67, 79, 89, 97, 127, 137, 149, 157, 163, 173, 179, 191, 211, 223, 239, 251, 257, 263, 269, 277, 293, 307, 331, 337, 347, 359, 367, 373, 379, 389, 397, 409, 419, 431, 439, 449, 457, 479, 487, 499, 509, 521, 541, 547, 557, 563, 569, 577, 587

Offset: 1

Enoch Haga, Oct 08 2007

Upper primes after a prime gap of 6 or larger (Union of A031925, A031927, A031929, ...) - R. J. Mathar, Mar 15 2012

			29 is a term because 29 follows the odd nonprime 27 which in turn follows the odd nonprime 25.

Bill McEachen, Table of n, a(n) for n = 1..10000

Cf. A007510, A083370, A124582, A134099, A134101, A073830.

Select[Range[5,1000,2],PrimeQ[#]&&!PrimeQ[#-2]&&!PrimeQ[#-4]&] (* Vladimir Joseph Stephan Orlovsky, Feb 03 2012 *)

forprime(p=5,600,if(!isprime(p-2) && !isprime(p-4), print1(p,", "))); \\ Joerg Arndt, Oct 27 2021

list(lim)=my(v=List(),p=23); forprime(q=29,lim, if(q-p>4, listput(v,q)); p=q); Vec(v) \\ Charles R Greathouse IV, Oct 27 2021

a(n) ~ n log n. - Charles R Greathouse IV, Oct 27 2021

Name corrected by Michel Marcus and Amiram Eldar, Oct 27 2021

A086138 Number of primes between p and p+10 if both p and (p+10) are prime, i.e., number of primes somewhere between 10+A023203(n) and A023203(n).

Original entry on oeis.org

3, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 0, 1, 1, 0, 2, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 1, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 0, 2, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2

Offset: 1

Labos Elemer, Jul 29 2003

nonn

			a(n)=0,1,2,3 correspond to {p,p+10} prime-pairs either consecutive ones or those with various d-patterns like as follows: a(n)=0 to cases like 139[10]149; a(n)=2 to 7[4,2,4]17 etc.; a(n)=3 to one case 3[2,2,4,2]13 and a(n)=2 to cases like 31[6,4]37 or 43[4,6]53.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A023303, A031928, A031929.

cp[x_,y_] := Count[Table[PrimeQ[i],{i,x,y}],True] Do[s=Prime[n]; s1=Prime[n+1]; If[PrimeQ[s+d],k=k+1; Print[cp[s+1,s+d-1]]],{n,1,1000}]; k; d=10
Count[Range[#+1,#+9],?PrimeQ]&/@Select[Prime[Range[500]],PrimeQ[#+10]&] (* _Harvey P. Dale, Jan 17 2025 *)

forprime(p=2,1e5,if(isprime(p+10), print1(isprime(p+2)+isprime(p+4)+isprime(p+6)+isprime(p+8)", "))) \\ Charles R Greathouse IV, May 15 2013

Definition clarified by Harvey P. Dale, Jan 17 2025

A333200 Rectangular array read by antidiagonals: row n shows the primes p(k) such that p(k) = p(k-1) + 2n, with 2 prefixed to row 1.

Original entry on oeis.org

2, 3, 11, 5, 17, 29, 7, 23, 37, 97, 13, 41, 53, 367, 149, 19, 47, 59, 397, 191, 211, 31, 71, 67, 409, 251, 223, 127, 43, 83, 79, 457, 293, 479, 307, 1847, 61, 101, 89, 487, 347, 521, 331, 1949, 541, 73, 107, 137, 499, 419, 631, 787, 2129, 1087, 907, 103, 113

Offset: 1

Clark Kimberling, May 09 2020

Every prime occurs exactly once.
Row 1: A001632, except for initial term
Row 2: A046132
Row 3: A031925
Row 4: A031927
Row 5: A031929
Column 1: A006512, beginning with 5,7,13

			Northwest corner:
    2   3     5    7   13   19   31   43   61   73  103
   11   17   23   41   47   71   83  101  107  113  131
   29   37   53   59   67   79   89  137  157  163  173
   97  367  397  409  457  487  499  691  709  727  751
  149  191  251  293  347  419  431  557  587  641  701

Cf. A333201, A000040, A001632, A006512.

z = 2700; p = Prime[Range[z]];
r[n_] := Select[Range[z], p[[#]] - p[[# - 1]] == 2 n &]; r[1] = Join[{1, 2}, r[1]];
TableForm[Table[Prime[r[n]], {n, 1, 18}]]  (* A333200, array *)
TableForm[Table[r[n], {n, 1, 18}]] (* A333201, array *)
Table[Prime[r[n - k + 1][[k]]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333200, sequence *)
Table[r[n - k + 1][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333201, sequence *)

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A134100 Primes p > 3 such that neither p-2 nor p-4 are prime.

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A086138 Number of primes between p and p+10 if both p and (p+10) are prime, i.e., number of primes somewhere between 10+A023203(n) and A023203(n).

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A333200 Rectangular array read by antidiagonals: row n shows the primes p(k) such that p(k) = p(k-1) + 2n, with 2 prefixed to row 1.

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