A284496 a(n) is the least number such that bigomega(a(n)) = bigomega(R(a(n)))/n, where R(n) is the digit reverse of n and bigomega(n) is the number of prime divisors of n counted with multiplicity.

2, 19, 29, 61, 23, 487, 821, 2557, 2749, 4201, 25747, 61843, 211643, 614881, 238673, 272059, 270131, 405719, 8239969, 42037283, 44922991, 44166589, 67719697, 61277761, 253442899, 2321783617, 4471131827, 4640384471, 40782386369, 4055086219, 25135138387, 63558323051

Offset

1,1

Comments

All values are prime.

Links

Table of n, a(n) for n=1..32.

Formula

Solutions of the equation A001222(n) = A001222(A004086(n))/n.

Example

bigomega(2) = 1. Its digit reverse is again 2 and bigomega(2) = 1 = 1 * 1;
bigomega(19) = 1 and bigomega(91) = 2 = 2 * 1;
bigomega(29) = 1 and bigomega(92) = 3 = 3 * 1;
bigomega(61) = 1 and bigomega(16) = 4 = 4 * 1; etc.

Maple

with(numtheory): R:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
P:=proc(q) local k, n; for k from 1 to q do for n from 2 to q do
if k*bigomega(n)=bigomega(R(n)) then print(n); break; fi; od; od; end: P(10^9);

Mathematica

rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; a[n_] := Block[{k, v}, For[k=2, Mod[v = PrimeOmega@ rev@ k, n] > 0 || v != n PrimeOmega@ k, k++]; k]; Array[a, 12] (* Giovanni Resta, Mar 29 2017 *)

Prog

(PARI) genit(maxx)={for(num=1, maxx, soln=0; forprime(p=2, 9E20, f=Vecrev(Str(p)); g=eval(concat(f)); if(bigomega(g)==num, print(num, "  ", p); soln=1; break)); if(soln<1, print("increase max prime"))); } \\ Bill McEachen, Mar 30 2017

Crossrefs

Cf. A001222, A004086, A284495, A284497, A284498.

Sequence in context: A102617 A365235 A290163 * A120276 A006962 A261312

Adjacent sequences: A284493 A284494 A284495 * A284497 A284498 A284499

Keyword

nonn,base

Author

Paolo P. Lava, Mar 28 2017

Extensions

a(23)-a(32) from Giovanni Resta, Mar 29 2017

a(26) corrected by Bill McEachen, Mar 30 2017

Status

approved