Revision History for A257638
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#14 by Alois P. Heinz at Wed Mar 08 04:00:26 EST 2023
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#13 by Joerg Arndt at Wed Mar 08 02:28:30 EST 2023
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#12 by Michel Marcus at Wed Mar 08 01:35:21 EST 2023
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#11 by Michel Marcus at Wed Mar 08 01:35:06 EST 2023
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Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html"> ">Twin Primes</a>
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approved
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#10 by N. J. A. Sloane at Tue Nov 17 19:17:28 EST 2015
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#9 by N. J. A. Sloane at Tue Nov 17 19:17:03 EST 2015
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| NAME
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Numbers n such wherethat n-25, n-1, n+1 and n+25 are consecutive primes.
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proposed
editing
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Discussion
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| Tue Nov 17
| 19:17
| N. J. A. Sloane: "such that" sounds better, I think
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#8 by Karl V. Keller, Jr. at Wed Nov 04 17:58:06 EST 2015
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#7 by Karl V. Keller, Jr. at Wed Nov 04 17:55:13 EST 2015
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| PROG
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.. ..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-25 and nextprime(i+1) == i+25: print (i, end=', ')
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#6 by Karl V. Keller, Jr. at Wed Nov 04 17:53:27 EST 2015
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Karl V. Keller, Jr., <a href="/A257638/b257638.txt">Table of n, a(n) for n = 1..10000</a>
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#5 by Karl V. Keller, Jr. at Wed Nov 04 17:49:58 EST 2015
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allocatedNumbers forn Karlwhere V. Kellern-25, n-1, Jrn+1 and n+25 are consecutive primes.
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| DATA
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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
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| OFFSET
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1,1
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| COMMENTS
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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).
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| LINKS
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Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html"> Twin Primes</a>
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| EXAMPLE
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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.
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| PROG
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(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-25 and nextprime(i+1) == i+25: print (i, end=', ')
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| CROSSREFS
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Cf. A014574, A077800 (twin primes), A249674, A256753.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Karl V. Keller, Jr., Nov 04 2015
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| STATUS
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approved
editing
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