A139025 This is to A014688 as A014688 to A000027, see comments for definition.

4, 7, 14, 23, 84, 107, 120, 135, 172, 183, 234, 283, 396, 433, 446, 519, 588, 617, 638, 661, 680, 695, 706, 725, 758, 783, 854, 891, 1000, 1043, 1064, 1119, 1226, 1283, 1458, 1469, 1490, 1521, 1618, 1661, 1708, 1765, 2046, 2157, 2224, 2333, 2428, 2507, 2516

Offset: 1

Author

Zak Seidov, Apr 07 2008

Keywords

• nonn

Comments

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 first 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

Crossrefs

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

Formula

A139025(n)=n+A061068(n)