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
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.
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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
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.
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Mean/@Select[Partition[Prime[Range[472000]],4,1],Differences[#] == {40,2,40}&] (* Harvey P. Dale, Oct 16 2021 *)
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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
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.
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Select[Partition[Prime[Range[500000]],4,1],Differences[#]=={34,2,34}&] [[All, 2]]+1 (* Harvey P. Dale, Oct 11 2017 *)
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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
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.
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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
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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
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.
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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
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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
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.
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Mean/@Select[Partition[Prime[Range[2325200]],4,1],Differences[#]=={48,2,48}&] (* Harvey P. Dale, Feb 10 2024 *)
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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
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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
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.
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Select[Partition[Prime[Range[122*10^5]],4,1],Differences[#]=={52,2,52}&][[All,2]]+1 (* Harvey P. Dale, Mar 07 2018 *)
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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=', ')
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