Records and first position of records in A088434. by Michael Thomas De Vlieger, St. Louis, MO 201708242120. k = record-setting value in A088434. m = first position in A088434 of k. m followed by "h" appear in A002182. A054841(m) = multiplicity notation of m. "211" is read as 2^2 * 3 * 5 = 60. For the purposes of this analysis, A054841 is considered reversed vis a vis the OEIS sequence. n m k A054841(m) 1 1 h 0 0 2 6 h 1 11 3 12 h 2 21 4 24 h 4 31 5 48 h 6 41 6 60 h 8 211 7 96 9 51 8 120 h 14 311 9 180 h 16 221 10 240 h 21 411 11 360 h 28 321 12 480 30 511 13 720 h 42 421 14 840 h 44 3111 15 1080 48 331 16 1260 h 52 2211 17 1440 60 521 18 1680 h 66 4111 19 2160 72 431 20 2520 h 88 3211 21 3360 93 5111 22 4320 102 531 23 5040 h 132 4211 24 7560 h 148 3311 25 10080 h 186 5211 26 15120 h 222 4311 27 20160 h 248 6211 28 25200 h 264 4221 29 27720 h 268 32111 30 30240 312 5311 31 40320 320 7211 32 45360 h 333 4411 33 50400 h 372 5221 34 55440 h 402 42111 35 60480 416 6311 36 75600 444 4321 37 83160 h 448 33111 38 90720 468 5411 Conjectures: (All excepting m(0) = 0.) 1. Numbers in m are products of the first several consecutive primes. 2. Outside of m(1), the largest prime factor of m has multiplicity 1. 3. The multiplicities of prime factors p of m generally decrease or stay the same as p increases.