

A070027


Prime numbers whose initial, all intermediate and final iterated sums of digits are primes.


10



2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 83, 101, 113, 131, 137, 151, 173, 191, 223, 227, 241, 263, 281, 311, 313, 317, 331, 353, 401, 421, 443, 461, 599, 601, 641, 797, 821, 887, 911, 977, 1013, 1019, 1031, 1033, 1051, 1091, 1103, 1109, 1123, 1163, 1181, 1213
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OFFSET

1,1


COMMENTS

Subsequence of A046704 ; actually, exactly those numbers for which the orbit under A007953 is a subset of A046704.  M. F. Hasler, Jun 28 2009
Supersequences: A046704 is primes p with digit sum s(p) also prime; A207294 is primes p with s(p) and s(s(p)) also prime.
Disjoint sequences: A104213 is primes p with s(p) not prime; A207293 is primes p with s(p) also prime, but not s(s(p)); A213354 is primes p with s(p) and s(s(p)) also prime, but not s(s(s(p))); A213355 is smallest prime p with kfold digit sum s(s(..s(p)).)..)) also prime for all k < n, but not for k = n.  Jonathan Sondow, Jun 13 2012


REFERENCES

Glyn Harman, Counting Primes whose Sum of Digits is Prime, Journal of Integer Sequences, Vol. 15 (2012), Article #12.2.2


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000


EXAMPLE

599 is a term because 599, 5+9+9=23 and 2+3=5 are all prime. 2999 is a term because 2999, 2+9+9+9=29, 2+9=11 and 1+1=2 are all prime. See A062802 and A070026 for related comments.


MAPLE

P:=proc(i) local a, k, n, w; for n from 1 by 1 to i do a:=ithprime(n); while isprime(a) and floor(a/10)>0 do w:=0; k:=a; while k>0 do w:=w+k(trunc(k/10)*10); k:=trunc(k/10); od; a:=w; od; if isprime(a) then print(ithprime(n)); fi; od; end: P(1000);  Paolo P. Lava, Jul 30 2008


MATHEMATICA

dspQ[n_] := TrueQ[Union[PrimeQ[NestWhileList[Plus@@IntegerDigits[#] &, n, # > 9 &]]] == {True}]; Select[Prime[Range[200]], dspQ] (* Alonso del Arte, Aug 17 2011 *)


PROG

(PARI) isA070027(n)={ while(isprime(n), n<9 && return(1); n=vector(#n=eval(Vec(Str(n))), i, 1)*n~)} \\ M. F. Hasler, Jun 28 2009


CROSSREFS

Cf. A070026 (a supersequence), subsequences: A062802, A070028, A070029.
Cf. also A046704, A104213, A207293, A207294, A213354, A213355.
Sequence in context: A046704 A089392 A089695 * A207294 A156658 A118723
Adjacent sequences: A070024 A070025 A070026 * A070028 A070029 A070030


KEYWORD

base,easy,nonn


AUTHOR

Rick L. Shepherd, Apr 14 2002


STATUS

approved



