New Sequence(s)? (was: what defines A113495? )

[zak seidov]

Sequence (or two?)inspied by this thread:

Slowest increasing sequence of perfect powers with
first differences being prime numbers:
1,4,9,16,27,32,49,128,169,216,289,512,529,576,2197,
2304,2401,8192,8281,27000,29791,32400,50653,54872,
55225,85184,89401,90000,90601,110592,116281,116964,
161051,166464,274625,278784,389017,389376,390625,
1061208,1062961,1065024,1225043,1227664,1367631,
1373584,1419857,1425636,1428025,2097152,2111209.

First differences:
3,5,7,11,5,17,79,41,47,73,223,17,47,1621,107,97,5791,
89,18719,2791,2609,18253,4219,353,29959,4217,599,601,
19991,5689,683,44087,5413,108161,4159,110233,359,
1249,670583,1753,2063,160019,2621,139967,
5953,46273,5779,2389,669127,14057

Rf. A001597, A113495




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