A056938 Concatenate all the prime divisors in previous term (with repetition), starting at 49.

49, 77, 711, 3379, 31109, 132393, 344131, 1731653, 71143523, 11115771019, 31135742029, 717261644891, 11193431873899, 116134799345907, 3204751189066719, 31068250396355573, 62161149980213343, 336906794442245927, 734615161567701999, 31318836286194043641

Offset: 1

Author

Robert G. Wilson v, Sep 05 2000

Keywords

• nonn
• base

Comments

This sequence provides a record of the search for the home prime for 49.

This sequence has now been followed for 117 steps without a prime being reached (after which of course it would simply repeat).

Links

• Patrick De Geest, Table of n, a(n) for n = 1..119
• P. De Geest, Home Primes
• Eric Weisstein's World of Mathematics, Home Prime

Crossrefs

Cf. A006919, A037273, A037274, A037271, A238579.

Programs

Mathematica

g[n_] := (x = n; d = {}; While[FactorInteger[x] != {}, f = FactorInteger[x, FactorComplete -> True][[1, 1]]; x = x/f; AppendTo[d, IntegerDigits[f]]]; FromDigits[Flatten[d]]); NestList[g, 49, 25]
(* Second program: *)
NestList[FromDigits@ Flatten@ Map[IntegerDigits, FactorInteger[#] /. {p_, e_} /; p >= 1 :> If[p == 1, 1, ConstantArray[p, e]]] &, 49, 16] (* Michael De Vlieger, Apr 27 2017 *)

PARI

a=vector(35); a[1]=49; for(k=2,length(a), f=factor(a[k-1]); for(i=1,matsize(f)[1], l=10^ceil(log(f[i,1])/log(10)); for(j=1,f[i,2], a[k]=a[k]*l+f[i,1]))) \\ M. F. Hasler, Mar 09 2007

Extensions

b-file updated by Max Alekseyev, Nov 28 2017