1,1

Take some initial sequence s1 = a(1), a(2),...

then for new sequence s2 = b(1), b(2),.. we define

b(n) = n + (n-th prime in s1).

If s1 = A000027 then we clearly get A014688.

If s1 = A014688 = 3,5,8,11,16,19,24,27,32,39,42,49,54,57,62,69,76,79,86,91,94

then b(1) = 1 + 3 (because 3 is the 1st prime in s1)

b(2) = 2 + 5 (because 5 is the 2nd prime in s1)

b(3) = 3 + 11 (because 11 is the 3rd prime in s1)

b(4) = 4 + 19 (because 19 is the 4th prime in s1)

b(5) = 5 + 79 (because 79 is the 5th prime in s1),

resulting sequence is A139025

Repeating the same procedure we have next sequences:

A139026: 8,25,110,287,438,623,668,1291,2342,2813,3790,3863,4230,4663,4828,6377,7468

A139027: 1292,3865,4666,8973,13936,50339,57266,67597,72316,85343,110934,132941,147990

A139028:270240,375255,635282,1000695,2039428,2602013,3398274,3748771,4300120

A139029:43448724,59672019,102128690,113904945,145135734,169755139

A139025(n)=n+A061068(n)

Cf. A000027, A014688, A061068, A139026-A139029.

Sequence in context: A008370 A048241 A003404 this_sequence A128610 A094968 A049946

Adjacent sequences: A139022 A139023 A139024 this_sequence A139026 A139027 A139028

nonn

Zak Seidov (zakseidov(AT)yahoo.com), Apr 07 2008