A092831 -id:A092831 - cp's OEIS frontend

A092832 Prime Motzkin numbers (see A001006).

2, 127, 15511, 953467954114363

Offset: 1

Eric W. Weisstein, Mar 06 2004

Joel A. Henningsen, Sequences Modulo Primes and Finite State Automata, Master's Thesis, University of South Alabama (2019).
Eric Weisstein's World of Mathematics, Motzkin Number

a[0]=1;a[n_Integer]:=a[n]=a[n-1]+Sum[a[k]*a[n-2-k], {k, 0, n-2}];lst={};Do[If[PrimeQ[p=a[n]], AppendTo[lst, p]], {n, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

A277455 Arithmetic derivatives of the Motzkin numbers.

Original entry on oeis.org

0, 0, 1, 4, 6, 10, 20, 1, 36, 172, 2192, 3371, 1, 22327, 135561, 517656, 284492, 933118, 5446991, 24265724, 18238138, 93800069, 334654476, 1368408363, 2584589232, 1823879615, 25669818480, 41583822879, 1967330543, 29409700520, 1265785403, 3239855363874

Offset: 0

Paul Bedard, Oct 16 2016

nonn

Cf. A003415, A001006, A068329, A092831.

Table[If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]] &@ Hypergeometric2F1[(1 - n)/2, -n/2, 2, 4], {n, 0, 31}] (* Michael De Vlieger, Oct 17 2016, after Michael Somos at A003415 and Peter Luschny at A001006 *)

a(n) = A003415(A001006(n)).

a(n) = 1 for n in A092831.

More terms from Alois P. Heinz, Oct 16 2016

cp's OEIS Frontend

A092832 Prime Motzkin numbers (see A001006).

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