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.

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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

Views

Author

Karl V. Keller, Jr., Dec 11 2015

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-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).

Examples

			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.

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • 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-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

Views

Author

Karl V. Keller, Jr., Apr 17 2016

Keywords

Comments

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).

Examples

			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.

Links

Crossrefs

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

Programs

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

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.

Links

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.

Links

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.

Links

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.

Links

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.

Links

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.

Links

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.

Links

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=', ')

A289982 Lesser member p of twin primes in A054723 (Prime exponents of composite Mersenne numbers).

Original entry on oeis.org

41, 71, 101, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607, 1619, 1667, 1697, 1721, 1787, 1871, 1877
Offset: 1

Views

Author

Muniru A Asiru, Jul 17 2017

Keywords

Comments

2^p-1 is composite. p is the lesser of twin primes in A001359 and a prime exponent of a Mersenne number in A054723.

Examples

			p=41 is a member because 41 is a lesser of twin prime and 2^41 - 1 = 13367*164511353 is composite.
Similarly, p=227 is a member because 227 is a lesser of twin prime and 2^227 - 1 is composite.

Links

Crossrefs

Subsequence of A054723.
Cf. A001097, A001359, A006512, A077800.

Programs

  • GAP
    P1:=Difference(Filtered([1..100000],IsPrime),[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701,23209, 44497, 86243]);;
P2:=List([1..Length(P1)-1],i->[P1[i],P1[i+1]]);;
P3:=List(Positions(List(P2,i->i[2]-i[1]),2),i->P2[i][1]);
  • Mathematica
    Function[s, Flatten@ Map[s[[#, 1]] &, Position[Most@ s, d_ /; Quiet@ Differences@ d == {2}, {1}]]]@ Partition[#, 2, 1] &@ Select[Prime@ Range@ 360, ! PrimeQ[2^# - 1] &] (* Michael De Vlieger, Jul 17 2017 *)
Select[Partition[Module[{nn=20,mp},mp=MersennePrimeExponent[Range[nn]];Complement[Prime[Range[PrimePi[Last[mp]]]],mp]],2,1],#[[2]]-#[[1]]==2 && AllTrue[#,PrimeQ]&][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 10 2019 *)
  • PARI
    isok(n) = isprime(n) && isprime(n+2) && !isprime(2^n-1) && !isprime(2^(n+2)-1); \\ Michel Marcus, Jul 19 2017
Previous Showing 81-90 of 108 results. Next

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