A256753 -id:A256753 - cp's OEIS frontend

A259025 Numbers k such that k is the average of four consecutive primes k-11, k-1, k+1 and k+11.

420, 1050, 2028, 2730, 3582, 4230, 4242, 4272, 4338, 6090, 6132, 6690, 6792, 8220, 11058, 11160, 11970, 12252, 15288, 19542, 19698, 21588, 21600, 26892, 27540, 28098, 28308, 29400, 30840, 30870, 31080, 32412, 42072, 45318, 47808, 48120

Offset: 1

Karl V. Keller, Jr., Jun 16 2015

nonn

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 0 are congruent to 0 mod 30.
The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.

			For n=420: 409, 419, 421, 431 are consecutive primes (n-11=409, n-1=419, n+1=421, n+11=431).
For n=1050: 1039, 1049, 1051, 1061 are consecutive primes (n-11=1039, n-1=1049, n+1=1051, n+11=1061).

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A052376, A077800 (twin primes), A014574, A249674 (30n), A256753.

{p, q, r, s} = {2, 3, 5, 7}; lst = {}; While[p < 50000, If[ Differences[{p, q, r, s}] == {10, 2, 10}, AppendTo[lst, q + 1]]; {p, q, r, s} = {q, r, s, NextPrime@ s}]; lst (* Robert G. Wilson v, Jul 15 2015 *)
Mean/@Select[Partition[Prime[Range[5000]],4,1],Differences[#]=={10,2,10}&] (* Harvey P. Dale, Sep 11 2019 *)

is(n)=n%6==0&&isprime(n-11)&&isprime(n-1)&&isprime(n+1)&&isprime(n+11)&&!isprime(n-7)&&!isprime(n-5)&&!isprime(n+5)&&!isprime(n+7) \\ Charles R Greathouse IV, Jul 17 2015

from sympy import isprime,prevprime,nextprime
for i in range(0,50001,2):
  if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-11 and nextprime(i+1) == i+11 :  print (i,end=', ')

a(n) = A052376(n) + 11. - Robert G. Wilson v, Jul 15 2015

A257638 Numbers n such that n-25, n-1, n+1 and n+25 are consecutive primes.

Original entry on oeis.org

232962, 311712, 431832, 435948, 473352, 501342, 525492, 596118, 635388, 665922, 699792, 754182, 842448, 1013502, 1017648, 1036002, 1156848, 1255452, 1284738, 1306692, 1479912, 1516128, 1551732, 1560708, 1595928, 1659348, 1690572, 1745112

Offset: 1

Karl V. Keller, Jr., Nov 04 2015

nonn

This is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.
The numbers n-25 and n+1 belong to A033560 (p and p+24 are primes) and A098974 (p where p+24 is the next prime).
The numbers n-25 and n-1 belong to A252089 (p and p+26 are primes).

			232962 is the average of the four consecutive primes 232937, 232961, 232963, 232987.
311712 is the average of the four consecutive primes 311687, 311711, 311713, 311737.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A249674, A256753.

from sympy import isprime,prevprime,nextprime
for i in range(0,1000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-25 and nextprime(i+1) == i+25: print (i,end=', ')

A258088 Numbers n such that n is the average of four consecutive primes n-5, n-1, n+1 and n+5.

Original entry on oeis.org

12, 18, 42, 102, 108, 228, 312, 462, 858, 882, 1092, 1302, 1428, 1488, 1872, 1998, 2688, 3462, 4518, 4788, 5232, 5652, 6828, 7878, 8292, 10458, 13692, 13878, 15732, 16062, 16068, 16188, 17388, 19422, 19428, 20748, 21018, 21318, 22278, 23058

Offset: 1

Karl V. Keller, Jr., May 19 2015

nonn

Previous name was: Numbers n such that n is the average of some twin prime pair p, q (q=p+2) (i.e., n=p+1=q-1) where p-4, p, q, and q+4 are consecutive primes.

This is a subsequence of A014574 (average of twin prime pairs) and A256753.

			12 is the average of the four consecutive primes 7, 11, 13, 17.
18 is the average of the four consecutive primes 13, 17, 19, 23.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A052378, A077800 (twin primes), A256753.

a={};Do[If[Prime[x + 3] - Prime[x]==10, AppendTo[a, Prime[x]+ 5]], {x, 1, 4000}]; a (* Vincenzo Librandi, Jul 18 2015 *)
Mean/@Select[Partition[Prime[Range[3000]],4,1],Differences[#]=={4,2,4}&] (* Harvey P. Dale, Sep 18 2018 *)

is(n)=isprime(n-5)&&isprime(n-1)&&isprime(n+1)&&isprime(n+5) \\ Charles R Greathouse IV, Aug 28 2015

from sympy import isprime,prevprime,nextprime
for i in range(0,50001,2):
  if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-5 and nextprime(i+1) == i+5: print (i,end=', ')

a(n) = A052378(n) + 5. - Karl V. Keller, Jr., Jul 17 2015

New name from Karl V. Keller, Jr., Jul 21 2015

A258879 Numbers k such that k is the average of four consecutive primes k-7, k-1, k+1 and k+7.

Original entry on oeis.org

30, 60, 270, 570, 600, 1230, 1290, 1620, 2340, 2550, 3540, 4020, 4650, 5850, 6270, 6360, 6570, 10860, 11490, 14550, 15270, 17490, 19080, 19380, 19470, 23670, 26730, 29130, 32370, 34260, 41610, 48480, 49200, 49530, 51420, 51480

Offset: 1

Karl V. Keller, Jr., Jun 13 2015

nonn

This sequence is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30*n).

			For k=30: 23, 29, 31, 37 are consecutive primes (k-7=23, k-1=29, k+1=31, k+7=37).
For k=60: 53, 59, 61, 67 are consecutive primes (k-7=53, k-1=59, k+1=61, k+7=67).

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A078854, A249674, A256753.

[n: n in [13..2*10^5] | IsPrime(n-7) and IsPrime(n-1) and IsPrime(n+1) and IsPrime(n+7)]; // Vincenzo Librandi Jul 16 2015

Select[ 5 Range@ 11000, PrimeQ[# - 7] && PrimeQ[# - 1] && PrimeQ[# + 1] && PrimeQ[# + 7] &] (* Robert G. Wilson v, Jun 28 2015 *)

main(size)={my(v=vector(size),i,t=8);for(i=1,size,while(1,if(isprime(t-7)&&isprime(t-1)&&isprime(t+1)&&isprime(t+7),v[i]=t;break,t++));t++);return(v);} /* Anders Hellström, Jul 17 2015 */

from sympy import isprime, prevprime, nextprime
for i in range(0, 10001, 2):
  if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-7 and nextprime(i+1) == i+7: print(i, end=', ')

a(n) = A078854(n) + 7.

A260959 Numbers n such that n is the average of four consecutive primes n-13, n-1, n+1 and n+13.

Original entry on oeis.org

7950, 10500, 32970, 33330, 34470, 36900, 43050, 66360, 71550, 74610, 87120, 89070, 92400, 94560, 95190, 102000, 104310, 121950, 125790, 133980, 148470, 156900, 160710, 168630, 174930, 182640, 194070, 204600, 206250, 230340, 244380, 246510

Offset: 1

Karl V. Keller, Jr., Aug 06 2015

nonn

This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).

			7950 is the average of the four consecutive primes 7937, 7949, 7951, 7963.
10500 is the average of the four consecutive primes 10487, 10499, 10501, 10513.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A249674, A256753.

use ntheory ":all"; say join ", ", map { $+1 } grep { next_prime($+2)-$==14 } grep { $-prev_prime($)==12 } @{twin_primes(1e6)}; # _Dana Jacobsen, Oct 03 2015

from sympy import isprime,prevprime,nextprime
for i in range(0,300001,2):
   if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-13 and nextprime(i+1) == i+13 :  print (i,end=', ')

A262176 Numbers k such that k-17, k-1, k+1 and k+17 are consecutive primes.

Original entry on oeis.org

3390, 66570, 70140, 84810, 132330, 136710, 222840, 225750, 242730, 271770, 288930, 320010, 330330, 377370, 390390, 414330, 463890, 489960, 505710, 644670, 758340, 819390, 830310, 857010, 895650, 906540, 908910, 924810, 952380, 968520, 974820

Offset: 1

Karl V. Keller, Jr., Sep 13 2015

nonn

This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).

			3390 is the average of the four consecutive primes 3373, 3389, 3391, 3407.
66570 is the average of the four consecutive primes 66553, 66569, 66571, 66587.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A249674, A256753.

Select[Prime@ Range@ 50000, NextPrime[#, {1, 2, 3}] == {16, 18, 34} + # &] + 17 (* Giovanni Resta, Sep 14 2015 *)

list(l)=for(i=1,l,my(p=prime(i)); if(p+16==prime(i+1) && p+18==prime(i+2) && p+34==prime(i+3), print1(p+17,", "))) \\ Anders Hellström, Sep 14 2015

use ntheory ":all"; say $+1 for grep { next_prime($+2)-$ == 18 && $-prev_prime($) == 16} @{twin_primes(1e9)}; # _Dana Jacobsen, Oct 13 2015

use ntheory ":all"; say $+17 for grep { next_prime($+0)-$ == 16 && next_prime($+18)-$ == 34} sieve_prime_cluster(1,1e9,16,18,34); # _Dana Jacobsen, Oct 13 2015

from sympy import isprime,prevprime,nextprime
for i in range(0,3000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1)==i-17 and nextprime(i+1)==i+17 : print (i,end=', ')

A262668 Numbers n such that n-19, n-1, n+1 and n+19 are consecutive primes.

Original entry on oeis.org

20982, 28182, 51768, 57222, 76422, 87720, 90678, 104850, 108108, 110730, 141180, 199602, 227112, 248118, 264600, 268842, 304392, 304458, 320082, 322920, 330018, 382728, 401670, 414432, 429972, 450258, 467082, 489408, 520548, 535608, 540120

Offset: 1

Karl V. Keller, Jr., Sep 26 2015

nonn

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 0 are divisible by 30 (cf. A249674).
The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.

			20982 is the average of the four consecutive primes 20963, 20981, 20983, 21001.
28182 is the average of the four consecutive primes 28163, 28181, 28183, 28201.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A249674, A256753.

Select[Range[6, 600000, 6], And[AllTrue[{# - 1, # + 1}, PrimeQ], NextPrime[# - 1, -1] == # - 19, NextPrime[# + 1] == # + 19] &] (* Michael De Vlieger, Sep 27 2015, Version 10 *)
Select[Prime@Range@60000, NextPrime[#, {1, 2, 3}] == {18, 20, 38} + # &] + 19 (* Vincenzo Librandi, Oct 10 2015 *)
Mean/@Select[Partition[Prime[Range[50000]],4,1],Differences[#]=={18,2,18}&] (* Harvey P. Dale, Jan 16 2019 *)

from sympy import isprime,prevprime,nextprime
for i in range(0,1000001,6):
  if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-19 and nextprime(i+1) == i+19 : print(i,end=', ')

A263298 Numbers n such that n-23, n-1, n+1 and n+23 are consecutive primes.

Original entry on oeis.org

19890, 43890, 157770, 400680, 436650, 609780, 681090, 797310, 924360, 978180, 1093200, 1116570, 1179150, 1185930, 1313700, 1573110, 1663350, 2001510, 2110290, 2163570, 2336310, 2372370, 2408280, 2415630, 2562690, 2877840, 2896740, 2961900

Offset: 1

Karl V. Keller, Jr., Oct 13 2015

nonn

This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).
From Michel Marcus, Oct 15 2015: (Start)
n-23 and n+1 belong to A242476 (p and p+22 are primes).
n-23 and n-1 belong to A033560 (p and p+24 are primes).
(End)

			19890 is the average of the four consecutive primes 19867, 19889, 19891, 19913.
43890 is the average of the four consecutive primes 43867, 43889, 43891, 43913.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A249674, A256753.

{p, q, r, s} = {2, 3, 5, 7};lst={}; While[p<5000000, If[Differences[{p, q, r, s}]=={22, 2, 22}, AppendTo[lst, q + 1]]; {p, q, r, s}={q, r, s,NextPrime@s}]; lst (* Vincenzo Librandi, Oct 14 2015 *)

isok(n) = isprime(n-1) && isprime(n+1) && (precprime(n-2) == n-23) && (nextprime(n+2) == n+23); \\ Michel Marcus, Oct 14 2015

from sympy import isprime,prevprime,nextprime
for i in range(0,5000001,6):
  if  isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-23 and nextprime(i+1) == i+23: print (i,end=', ')

A265651 Numbers n such that n-29, n-1, n+1 and n+29 are consecutive primes.

Original entry on oeis.org

14592, 84348, 151938, 208962, 241392, 254490, 397182, 420192, 494442, 527700, 549978, 581982, 637200, 641550, 712602, 729330, 791628, 850302, 975552, 995052, 1086558, 1107852, 1157670, 1245450, 1260798, 1286148, 1494510, 1555290, 1608912

Offset: 1

Karl V. Keller, Jr., Dec 11 2015

nonn

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 0 are divisible by 30 (cf. A249674).
The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.
The numbers n-29 and n+1 belong to A252090 (p and p+28 are primes) and A124595 (p where p+28 is the next prime).
The numbers n-29 and n-1 belong to A049481 (p and p+30 are primes).

			14592 is the average of the four consecutive primes 14563, 14591, 14593, 14621.
84348 is the average of the four consecutive primes 84319, 84347, 84349, 84377.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A249674, A256753.

Select[Prime@Range@100000, NextPrime[#, {1, 2, 3}] == {28, 30, 58} + # &] + 29 (* Vincenzo Librandi, Dec 12 2015 *)
Mean/@Select[Partition[Prime[Range[125000]],4,1],Differences[#]=={28,2,28}&] (* Harvey P. Dale, May 02 2016 *)

from sympy import isprime,prevprime,nextprime
for i in range(0,1000001,6):
   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-29 and nextprime(i+1) == i+29 :  print (i,end=', ')

A268305 Numbers k such that k - 37, k - 1, k + 1, k + 37 are consecutive primes.

Original entry on oeis.org

1524180, 3264930, 3970530, 5438310, 5642910, 6764940, 8176410, 10040880, 10413900, 10894320, 11639520, 12352980, 13556340, 15900720, 16897590, 17283360, 18168150, 18209100, 18686910, 19340220, 20099940, 20359020, 20483340, 21028290, 21846360

Offset: 1

Karl V. Keller, Jr., Apr 17 2016

nonn

This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
The numbers k - 37 and k + 1 belong to A156104 (p and p + 36 are primes) and A134117 (p where p + 36 is the next prime).
The numbers k - 37 and k - 1 belong to A271347 (p and p + 38 are primes).

			1524180 is the average of the four consecutive primes 1524143, 1524179, 1524181, 1524217.
3264930 is the average of the four consecutive primes 3264893, 3264929, 3264931, 3264967.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes

Cf. A014574, A077800 (twin primes), A249674, A256753.

Select[Partition[Prime[Range[14*10^5]],4,1],Differences[#]=={36,2,36}&][[All,2]]+1 (* Harvey P. Dale, Mar 12 2018 *)

from sympy import isprime,prevprime,nextprime
for i in range(0,30000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-37 and nextprime(i+1) == i+37 : print (i,end=', ')

cp's OEIS Frontend

A259025 Numbers k such that k is the average of four consecutive primes k-11, k-1, k+1 and k+11.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A257638 Numbers n such that n-25, n-1, n+1 and n+25 are consecutive primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

A258088 Numbers n such that n is the average of four consecutive primes n-5, n-1, n+1 and n+5.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

Extensions

A258879 Numbers k such that k is the average of four consecutive primes k-7, k-1, k+1 and k+7.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

Formula

A260959 Numbers n such that n is the average of four consecutive primes n-13, n-1, n+1 and n+13.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Perl

Python

A262176 Numbers k such that k-17, k-1, k+1 and k+17 are consecutive primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Perl

Perl

Python

A262668 Numbers n such that n-19, n-1, n+1 and n+19 are consecutive primes.

Views

Author