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.

Previous Showing 11-17 of 17 results.

A270754 Numbers n such that n - 31, n - 1, n + 1 and n + 31 are consecutive primes.

Original entry on oeis.org

90438, 258918, 293862, 385740, 426162, 532950, 1073952, 1317192, 1318410, 1401318, 1565382, 1894338, 1986168, 2174772, 2612790, 2764788, 3390900, 3450048, 3618960, 3797250, 3961722, 3973062, 4074870, 4306230, 4648068, 4917360, 5351010, 5460492
Offset: 1

Views

Author

Karl V. Keller, Jr., Mar 22 2016

Keywords

Comments

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 - 31 and n + 1 belong to A049481 (p and p + 30 are primes) and A124596 (p where p + 30 is the next prime).
The numbers n - 31 and n - 1 belong to A049489 (p and p + 32 are primes).

Examples

			90438 is the average of the four consecutive primes 90407, 90437, 90439, 90469.
258918 is the average of the four consecutive primes 258887, 258917, 258919, 258949.
		

Crossrefs

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

Programs

  • Python
    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-31 and nextprime(i+1) == i+31 :  print (i,end=', ')

A271323 Numbers n such that n - 41, n - 1, n + 1, n + 41 are consecutive primes.

Original entry on oeis.org

383220, 1269642, 1528938, 2590770, 3014700, 3158298, 3697362, 3946338, 4017312, 4045050, 4545642, 4711740, 4851618, 4871568, 5141178, 5194602, 5925042, 5972958, 5990820, 6075030, 6179862, 6212202, 6350760, 6442938, 6549312, 6910638, 6912132
Offset: 1

Views

Author

Karl V. Keller, Jr., May 15 2016

Keywords

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 0 belong to A249674 (divisible by 30).
The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.
The numbers n - 40 and n + 1 belong to A126721 (p such that p + 40 is the next prime) and A271981 (p and p + 40 are primes).
The numbers n - 40 and n - 1 belong to A271982 (p and p + 42 are primes).

Examples

			383220 is the average of the four consecutive primes 383179, 383219, 383221, 383261.
1269642 is the average of the four consecutive primes 1269601, 1269641, 1269643, 1269683.
		

Crossrefs

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

Programs

  • Mathematica
    Mean/@Select[Partition[Prime[Range[472000]],4,1],Differences[#] == {40,2,40}&] (* Harvey P. Dale, Oct 16 2021 *)
  • Python
    from sympy import isprime,prevprime,nextprime
    for i in range(0,12000001,6):
      if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-41 and nextprime(i+1) == i+41: print (i,end=', ')

A271349 Numbers n such that n - 35, n - 1, n + 1 and n + 35 are consecutive primes.

Original entry on oeis.org

276672, 558828, 1050852, 1278288, 1486908, 1625418, 2536308, 2538918, 2690958, 2731242, 3015162, 3252678, 3268338, 3508278, 3711612, 4233708, 4575912, 4717962, 5004402, 5108352, 5404032, 5482782, 5519082, 5525328, 5640918, 5654358, 5995818
Offset: 1

Views

Author

Karl V. Keller, Jr., Apr 04 2016

Keywords

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.
The numbers n - 35 and n + 1 belong to A252091 (p and p + 34 are primes) and A134116 (p such that p + 34 is the next prime).
The numbers n - 35 and n - 1 belong to A156104 (p and p + 36 are primes).

Examples

			276672 is the average of the four consecutive primes 276637, 276671, 276673, 276707.
558828 is the average of the four consecutive primes 558793, 558827, 558829, 558863.
		

Crossrefs

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

Programs

  • Mathematica
    Select[Partition[Prime[Range[500000]],4,1],Differences[#]=={34,2,34}&] [[All, 2]]+1 (* Harvey P. Dale, Oct 11 2017 *)
  • Python
    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-35 and nextprime(i+1) == i+35 :  print (i,end=', ')

A273101 Numbers n such that n - 43, n - 1, n + 1, n + 43 are consecutive primes.

Original entry on oeis.org

7714800, 8126820, 8341260, 8646060, 9200880, 9422970, 13224270, 13597920, 14012460, 14124630, 15305700, 17008680, 17563920, 18830940, 22603740, 22812150, 24576240, 25197300, 26147040, 26196900, 26932950, 27225240, 30305580, 31214640
Offset: 1

Views

Author

Karl V. Keller, Jr., May 15 2016

Keywords

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
The numbers n - 43 and n + 1 belong to A272176 (p and p + 44 are primes) and A134120 (p such that p + 42 is the next prime).
The numbers n - 43 and n - 1 belong to A271982 (p and p + 42 are primes).

Examples

			7714800 is the average of the four consecutive primes 7714757, 7714799, 7714801, 7714843.
8126820 is the average of the four consecutive primes 8126777, 8126819, 8126821, 8126863.
		

Crossrefs

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

Programs

  • PARI
    is(n)=n%30==0 && isprime(n-1) && isprime(n+1) && nextprime(n+2)==n+43 && precprime(n-2)==n-43 \\ Charles R Greathouse IV, May 15 2016
  • Python
    from sympy import isprime,prevprime,nextprime
    for i in range(0,60000001,6):
      if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-43 and nextprime(i+1) == i+43: print (i,end=', ')
    

A273355 Numbers n such that n - 47, n - 1, n + 1, n + 47 are consecutive primes.

Original entry on oeis.org

15370470, 15462870, 18216510, 23726160, 30637050, 31054740, 38907060, 39220080, 44499900, 44678190, 60563100, 66248550, 86219910, 87095190, 87948780, 93773970, 96802860, 103011990, 105953760, 105978330, 106960410, 111219990, 116281770
Offset: 1

Views

Author

Karl V. Keller, Jr., May 20 2016

Keywords

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
The numbers n - 47 and n + 1 belong to A134122 (p such that p + 46 is the next prime).
The numbers n - 47 and n - 1 belong to primes p such that p and p + 48 are primes.

Examples

			15370470 is the average of the four consecutive primes 15370423, 15370469, 15370471, 15370517.
15462870 is the average of the four consecutive primes 15462823, 15462869, 15462871, 15462917.
		

Crossrefs

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

Programs

  • PARI
    is(n)=isprime(n-1) && isprime(n+1) && precprime(n-2)==n-47 && nextprime(n+2)==n+47 \\ Charles R Greathouse IV, Jun 08 2016
  • Python
    from sympy import isprime,prevprime,nextprime
    for i in range(0,160000001,6):
      if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-47 and nextprime(i+1) == i+47: print (i,end=', ')
    

A273356 Numbers n such that n - 49, n - 1, n + 1, n + 49 are consecutive primes.

Original entry on oeis.org

913638, 2763882, 4500492, 6220518, 6473148, 13884468, 15131982, 15729942, 19671930, 20494602, 21372888, 23791350, 25541028, 29535348, 30787788, 30906768, 32085372, 34128168, 34139802, 34550430, 35989980, 37473180, 37784310, 38106372
Offset: 1

Views

Author

Karl V. Keller, Jr., May 20 2016

Keywords

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 0 belong to A249674 (divisible by 30).
The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.
The numbers n - 49 and n + 1 belong to A134123 (p such that p + 48 is the next prime).
The numbers n - 49 and n - 1 belong to A062284 (p and p + 50 are primes).

Examples

			913638 is the average of the four consecutive primes 913589, 913637, 913639, 913687.
2763882 is the average of the four consecutive primes 2763833, 2763881, 2763883, 2763931.
		

Crossrefs

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

Programs

  • Mathematica
    Mean/@Select[Partition[Prime[Range[2325200]],4,1],Differences[#]=={48,2,48}&] (* Harvey P. Dale, Feb 10 2024 *)
  • PARI
    is(n)=isprime(n-1) && isprime(n+1) && precprime(n-2)==n-49 && nextprime(n+2)==n+49 \\ Charles R Greathouse IV, Jun 08 2016
  • Python
    from sympy import isprime,prevprime,nextprime
    for i in range(0,60000001,6):
      if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-49 and nextprime(i+1) == i+49: print (i,end=', ')
    

A274042 Numbers k such that k - 53, k - 1, k + 1, k + 53 are consecutive primes.

Original entry on oeis.org

9401700, 64312710, 78563130, 83494350, 92978310, 101520540, 111105090, 121631580, 136765860, 138330780, 139027950, 145673850, 157008390, 163050090, 166418280, 169288530, 170473410, 177920850, 198963210, 200765250, 213504870, 220428600
Offset: 1

Views

Author

Karl V. Keller, Jr., Jun 07 2016

Keywords

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
The numbers n - 53 and n + 1 belong to A204665 (p such that p + 52 is the next prime).
The numbers n - 53 and n - 1 belong to primes p such that p + 54 is prime.

Examples

			9401700 is the average of the four consecutive primes 9401647, 9401699, 9401701, 9401753.
64312710 is the average of the four consecutive primes 64312657, 64312709, 64312711, 64312763.
		

Crossrefs

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

Programs

  • Mathematica
    Select[Partition[Prime[Range[122*10^5]],4,1],Differences[#]=={52,2,52}&][[All,2]]+1 (* Harvey P. Dale, Mar 07 2018 *)
  • Python
    from sympy import isprime,prevprime,nextprime
    for i in range(0,250000001,6):
      if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-53 and nextprime(i+1) == i+53: print (i,end=', ')
Previous Showing 11-17 of 17 results.