A062094
a(1) = 2, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
2, 12, 34, 217, 731, 1743, 2183, 3759, 21179, 121179, 931303, 1931303, 11175573, 11379829, 17896361, 18419721, 96919009, 889910891, 1889910891, 2742368917, 25741106537, 110203233579, 679231622473, 1679231622473, 7921256096487
Offset: 1
a(1) = 2 is a prime hence a(2) = 12; a(3) = 34, 3*4 = 12 and 3<4.
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f[n_Integer] := (d = Divisors[n]; l = Length[d]; If[ EvenQ[l], ToExpression[ ToString[ d[[l/2]] ] <> ToString[ d[[l/2 + 1]] ]], ToExpression[ ToString[d[[l/2 + .5]] ] <> ToString[ d[[l/2 + .5]] ]]] ); NestList[f, 2, 25]
A063383
a(1) = 6, a(n) = concatenation of two closest divisors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
6, 23, 123, 341, 1131, 2939, 12939, 57227, 89643, 329881, 1073083, 1197553, 7171079, 17171079, 57301247, 208327509, 1171780577, 1219684137, 1478297171, 2587571433, 2795835979, 8663322733, 13666409441, 113666409441, 1030771102733, 2114885171103, 6993025586797
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[[ l/2 ] ] ] <> ToString[ d[[ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[[ l/2 + .5 ] ] ] <> ToString[ d[[ l/2 + .5 ] ] ] ] ] ); NestList[ f, 6, 25 ]
tcf[n_]:=Module[{d=Divisors[n],len},len=Length[d]/2;FromDigits[Flatten[ IntegerDigits/@Take[d,{len,len+1}]]]]; ctc[n_]:=If[PrimeQ[ n], 10^IntegerLength[ n]+n,tcf[n]]; NestList[ctc,6,30] (* Harvey P. Dale, May 19 2019 *)
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from sympy import divisors, isprime
def aupton(terms):
alst = [6]
for n in range(2, terms+1):
if isprime(alst[-1]): alst.append(int('1' + str(alst[-1])))
else:
divs = divisors(alst[-1])
d1 = divs[(len(divs)-1)//2]
d2 = alst[-1]//d1
alst.append(int(str(d1) + str(d2)))
return alst
print(aupton(27)) # Michael S. Branicky, Jun 23 2021
A063269
a(1) = 3, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
3, 13, 113, 1113, 2153, 12153, 34051, 172003, 1311313, 3473779, 5365543, 16913173, 34014973, 229148537, 479347809, 1807726517, 11807726517, 20529575173, 69833293981, 179443389167, 230839777353, 376946592451
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 3, 24 ]
A063380
a(1) = 4, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
4, 22, 211, 1211, 7173, 9797, 97101, 910789, 1182799, 1319029, 6719687, 7678761, 32559587, 257126691, 1591617149, 6653239233, 62767105999, 126149775659, 432933715713, 2435717774509, 6598336914323, 19495633384521
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 4, 24 ]
A063382
a(1) = 5, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
5, 15, 35, 57, 319, 1129, 11129, 31359, 310453, 1691837, 7241691, 15094799, 31486929, 159198031, 1159198031, 6203186877, 11721529237, 88429132553, 129487682919, 1228291054211, 1394483927247, 8800411584567, 34329256355023
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 5, 24 ]
A063384
a(1) = 7, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
7, 17, 117, 913, 1183, 1391, 13107, 51257, 151257, 381397, 577661, 4911789, 29116879, 112646989, 536920981, 1928258999, 11928258999, 25227472837, 46275452231, 212892173679, 370964057893, 1859199550327, 5593332415439
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[[ l/2 ] ]] <> ToString[ d[[ l/2 + 1 ]] ]], ToExpression[ ToString[ d[[ l/2 + .5 ] ]] <> ToString[ d[[ l/2 + .5 ] ]] ]] ); NestList[ f, 7, 25 ]
A063403
a(1) = 8, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
8, 24, 46, 223, 1223, 11223, 87129, 189461, 414621, 2072003, 12072003, 34024001, 163920759, 354640253, 1074732999, 7377145687, 17377145687, 57053304579, 393145173803, 834736688841, 8062231035367, 26899299722333, 27745499695017
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[[ l/2 ] ]] <> ToString[ d[[ l/2 + 1 ]] ]], ToExpression[ ToString[ d[[ l/2 + .5 ] ]] <> ToString[ d[[ l/2 + .5 ] ]] ]] ); NestList[ f, 8, 25 ]
A063423
a(1) = 9, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
9, 33, 311, 1311, 2357, 12357, 91373, 191373, 273701, 594639, 966071, 3792549, 7714919, 18474177, 36158059, 217166627, 415296747, 1269327263, 8581147923, 85531003291, 307572780863, 417501775143, 594709702027, 1334471501519
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 9, 25 ]
A063424
a(1) = 10, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
10, 25, 55, 511, 773, 1773, 9197, 17541, 91949, 143643, 347881, 3311051, 13311051, 35433757, 71499067, 72619847, 74179791, 82678973, 613313481, 1551395431, 1679289793, 4339053251, 6529966449, 9370214693, 71338602099, 222407320757
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 10, 25 ]
Showing 1-9 of 9 results.