A011974 : Is 2 the sum of 2 successive primes?

[N. J. A. Sloane]

sequence, explain why this sequence starts with 2 (which is NOT the
sum of two successive primes) - perhaps there is a special reason for
Me:  check the reference that I give and you will see where
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From: "N. J. A. Sloane" <njas at research.att.com>
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To: rkg at cpsc.ucalgary.ca, seqfan at ext.jussieu.fr, seqfans at seqfan.net
Subject: Re: Two or three more sequences??
Cc: editors at seqfan.net
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Date: Tue, 19 Feb 2008 13:01:21 -0800 (PST)
From: zak seidov <zakseidov at yahoo.com>
Subject: Sums payable with change
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Let both customer and seller have unlimited number of
banknotes of DENOMINATIONs
(not NOMINALs as they say in Russian!)
1, 5, 10, 20, 50, and 100.

 Using exactly THREE banknotes (no change in seller's
cash, only customer pays), 
there are 52  payable in (A135137)
3,7,11,12,15,16,20,21,22,25,26,30,31,35,40,41,45,50,52,56,60,61,65,70,71,75,80,90,101,102,105,106,110,111,115,120,121,125,130,140,150,151,155,160,170,200,
201,205,210,220,250,300

Additionally there are 
43 sums payable with change:
0,1,4,5,6,8,9,10,14,18,19,24,29,39,44,46,48,49,51,54,55,59,69,79,81,85,89,91,94,95,96,98,99,100,104,109,119,145,149,180,190,195,199
e.g., 1=1+1-1 (customer pays two and gets back one),
5=20-10-5  (customer pays 20 and gets back 10 and 5),
109=100+10-1 (customer pays 100+10 and gets back 1).

Hence there are 52+43=95 sums payable  using exactly
THREE banknotes in the deal 
(i.e. with change allowable).

In the case of TWO banknotes there are 33 payable
sums: 
0, 2, 4, 5, 6, 9, 10, 11, 15, 19, 20, 21, 25, 30, 40,
45, 49, 50, 51, 55,60, 70, 80, 90, 95, 99, 100, 101,
105, 110, 120, 150, 200.

In the case of ONE banknote there are 6 payable sums
(no change as only ONE banknote available):
1,5,10,20,50,100.
Finally with ZERO banknote only one sum is possible,
namely zero.
Hence, the beginning of new suggested sequence is:
a(0)=1, a(1)=6, a(2)=33, a(3)=95.
Can anyone check/extend this?
thanks, zak
Cf. A124146, A135137, A135454 


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