A064821 Number of ways of writing the numbers 1 .. n in a sequence so that the sum of any two adjacent numbers is a prime; reversing the sequence does not count as different.

0, 1, 1, 4, 2, 8, 12, 30, 70, 664, 1072, 8768, 11648, 37108, 95772, 1059816, 2047488, 12111712, 22802028, 120779959, 337801784, 4361743860, 11425028900, 142573286216, 429917269469, 4138239848098, 16171519847028, 214845911686065

Offset

1,4

Comments

If the sequence is d_1 d_2 ... d_n then the n-1 sums d_i + d_{i+1} are required to be primes.

I conjecture a(n) > 0 for all n.

Variant of A051239 with respect to a(1). - R. J. Mathar, Oct 02 2008

Links

Table of n, a(n) for n=1..28.

Example

For n = 4 there are 4 sequences: 1234, 1432, 3214, 3412.

Crossrefs

Cf. A064821, A103839.

Sequence in context: A246202 A134042 A051239 * A002291 A225872 A231777

Adjacent sequences: A064818 A064819 A064820 * A064822 A064823 A064824

Keyword

nonn,nice

Author

N. J. A. Sloane, Oct 23 2001

Extensions

More terms from Jud McCranie, Oct 24 2001

a(22)-a(24) from Donovan Johnson, Aug 27 2010

a(25)-a(28) from Giovanni Resta, Jun 05 2020

Status

approved