A117300 Consider all pairs (p,q) of consecutive primes such that p and q both have k digits and q-p = k; sequence lists the values of q.

3, 13, 19, 31, 43, 61, 73, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433, 1451, 1487, 1493, 1553, 1571, 1583, 1601, 1613, 1667, 1697, 1787, 1871, 1877, 1997, 2003, 2087, 2141, 2207, 2243, 2273, 2297, 2351, 2381, 2393, 2441, 2477, 2543, 2621, 2663

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Example

31 is in the sequence because (1) it is a 2-digit prime number, (2) the previous 2-digit prime number is 29 and (3) 31-29=2
1451 is in the sequence because (1) it is a 4-digit prime number, (2) the previous 4-digit prime number is 1447 and (3) 1451-1447=4

Mathematica

Transpose[Select[Partition[Prime[Range[400]], 2, 1], IntegerLength[#[[1]]] == IntegerLength[#[[2]]]&&#[[2]]-#[[1]]==IntegerLength[#[[1]]]&]][[2]] (* Harvey P. Dale, Nov 01 2015 *)

Crossrefs

Cf. A117155.

Sequence in context: A168425 A252090 A079419 * A023215 A185069 A023239

Adjacent sequences: A117297 A117298 A117299 * A117301 A117302 A117303

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 21 2006

Extensions

Edited by N. J. A. Sloane, Apr 29 2007

Corrected by Harvey P. Dale, Nov 01 2015

Status

approved