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A089291
Prime worms (as defined below).
4
101, 787, 12101, 32323, 34543, 78787, 1012321, 1212121, 3212123, 3212323, 3454343, 7654567, 7656787, 7676567, 7678787, 7876567, 7898767, 101012321, 101210101, 101232121, 121232101, 123210121, 123232121, 321234343, 323232323
OFFSET
1,1
COMMENTS
By analogy, primes of this type are worms with a head and tail and body composed of the same digit which weaves in and out of the prime. In a(2)=12101 the worm is defined by the digit 1.
REFERENCES
The concept is due to Carlos Rivera in his Puzzle 246 (where he asks for the first pandigital prime worm and for the first pandigital titanic prime worm - solutions are at his site).
FORMULA
Primes whose first and last digits are identical and whose successive digit differences have a uniformly absolute value of 1. Thus the sum of absolute values is one less than the number of digits in the prime. No two adjacent digits are identical or differ by more than one.
EXAMPLE
a(2)=12101 because that number is prime with identical first and last digits. Then abs(1-2)=1; abs(2-1)=1; abs(1-0)=1; abs(0-1)=1; and sum of absolute values is 4, one less than the 5 digits in the prime.
CROSSREFS
This is a subset of A048398. Cf. A089315-A089317, A048398-A048405.
Sequence in context: A227521 A364147 A171813 * A167842 A244369 A200733
KEYWORD
nonn,base
AUTHOR
Enoch Haga, Dec 23 2003
EXTENSIONS
Edited by Charles R Greathouse IV, Aug 02 2010
STATUS
approved