A144249 -id:A144249 - cp's OEIS frontend

A128379 A000012^23 * A000594.

1, -1, -24, 0, 276, 300, -1748, -4300, 4278, 29026, 22724, -94668, -242398, -18722, 856980, 1472252, -384491, -5299269, -7824968, 2088032, 25655442, 38814478, -69160, -99735912, -175711283, -68736397, 294769680, 686373176, 562588924, -513324396, -2155273788, -2808874356

Offset: 1

Gary W. Adamson, Feb 28 2007

sign

Conjecture: given A000012^k * A000594, k=23 and 24 are the only k's generating sequences with zeros. k = 24 in A128378: (1, 0, -24, -24, 252, 552, -1196, -5496, ...).

Cf. A000594, A128378, A144248, A144249.

Nest[Accumulate, RamanujanTau[Range[32]], 23] (* Amiram Eldar, Jan 08 2025 *)

A000012 (partial sum operator) performed 23 times on A000594.

A280828 Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

Original entry on oeis.org

4, 22, 202

Offset: 1

Sergey Pavlov, Jan 08 2017

Let k=2*10^(n-1)+2, then a(n)=10^k+9. For all k>4, k is a term of A058441.
The only known terms from A088275 (Numbers n such that 10^n + 9 is prime) that are of the form 2*10^j + 2 are 4, 22, and 202; given the lower bound given for that sequence's next term, a(4) >= 200002. - Jon E. Schoenfield, Jan 11 2017
For n<4, let k=a(n) and p=(10^k-9)/10^(k/2)+3=10^(k/2)+3, then p is prime. - Sergey Pavlov, Jan 13 2017

			For n=1, a(1)=4 and 10^4 + 9 is prime.

Cf. A043037, A058441, A088275, A144249, A205529.

Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

cp's OEIS Frontend

A128379 A000012^23 * A000594.

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