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A308764
Table read by antidiagonals: T(n,k) is the smallest prime that differs from its predecessor and successor by 2n and 2k, respectively.
1
5, 7, 11, 31, 0, 29, 0, 23, 37, 0, 139, 401, 53, 97, 149, 199, 0, 89, 367, 0, 521, 0, 467, 337, 0, 251, 223, 0, 1933, 113, 509, 409, 701, 1543, 127, 1949, 523, 0, 953, 1201, 0, 479, 331, 0, 1277, 0, 2861, 3643, 0, 797, 631, 0, 3407, 1087, 0, 1951, 887, 1069, 1831, 293, 211, 787, 2609, 541, 907, 1151
OFFSET
1,1
COMMENTS
If two consecutive primes p and q appear in the table, then the column number in which p appears is the row number in which q appears. E.g., 23 is in column 3 and 29 is in row 3, 29 is in column 1 and 31 is in row 1, 113 is in column 7 and 127 is in row 7, 3643 is in column 8 and 3659 is in row 8.
Nonzero terms on the main diagonal are the terms of A054342.
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..5050 (first 100 antidiagonals, flattened)
FORMULA
T(n,k)=0 if n == k (mod 3) !== 0 (mod 3), with the exception of T(1,1)=5.
EXAMPLE
T(1,1)=5 because 5 is the only prime p whose predecessor and successor primes are p-2 and p+2, respectively (i.e., 3 and 7).
T(7,2)=127 because 127 is the smallest prime p whose predecessor and successor primes are p-14 and p+4, respectively (i.e., 113 and 131).
T(2,2)=0: the only set of three numbers {p-4, p, p+4} that are all prime is the set {3, 7, 11}, but these are not consecutive primes. (For every set of three integers {m-4, m, m+4}, exactly one of the three is divisible by 3.)
Table begins:
5, 7, 31, 0, 139, 199, 0, 1933, ...
11, 0, 23, 401, 0, 467, 113, 0, ...
29, 37, 53, 89, 337, 509, 953, 3643, ...
0, 97, 367, 0, 409, 1201, 0, 1831, ...
149, 0, 251, 701, 0, 797, 293, 0, ...
521, 223, 1543, 479, 631, 211, 2633, 4111, ...
0, 127, 331, 0, 787, 7057, 0, 13381, ...
1949, 0, 3407, 2609, 0, 3659, 1847, 0, ...
... ... ... ... ... ... ... ... ...
CROSSREFS
Cf. A000040 (primes), A001223 (prime gaps), A054342 (first occurrence of distances of equidistant lonely primes).
Sequence in context: A050299 A092029 A259564 * A288609 A156559 A018426
KEYWORD
nonn,tabl
AUTHOR
Jon E. Schoenfield, Jun 23 2019
STATUS
approved