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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 (list; graph; refs; listen; history; text; internal format)



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.


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).


Table of n, a(n) for n=1..25.

Carlos Rivera, Puzzle 246. The worms


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.


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.


This is a subset of A048398. Cf. A089315-A089317, A048398-A048405.

Sequence in context: A153806 A227521 A171813 * A167842 A244369 A200733

Adjacent sequences:  A089288 A089289 A089290 * A089292 A089293 A089294




Enoch Haga, Dec 23 2003


Edited by Charles R Greathouse IV, Aug 02 2010



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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)