A068952 -id:A068952 - cp's OEIS frontend

A068809 Squares with strictly increasing sum of digits.

1, 4, 9, 49, 169, 289, 1849, 3969, 6889, 27889, 69696, 97969, 499849, 698896, 2778889, 4999696, 9696996, 19998784, 46689889, 66699889, 79869969, 277788889, 478996996, 876988996, 1749999889, 5599977889, 7998976969, 8998988769, 17999978896

Offset: 1

Amarnath Murthy, Mar 06 2002

Giovanni Resta, Table of n, a(n) for n = 1..80 (first 57 terms from Kevin Buzzard)

Cf. A068947, A068948, A068949, A068950, A068952, A069324.

A007953 := proc(n) option remember: return add(d, d=convert(n, base, 10)): end: A068947 := proc(n) option remember: local k, p: if(n=1)then return 1: fi: k:=procname(n-1): p:=A007953(k^2): do k:=k+1: if(A007953(k^2)>p)then return k: fi: od: end: seq(A068947(n)^2, n=1..20); # Nathaniel Johnston, May 04 2011

t = {}; s = 0; Do[If[(x = Total[IntegerDigits[y = n^2]]) > s, AppendTo[t, y]; s = x], {n, 150000}]; t (* Jayanta Basu, Aug 06 2013 *)

More terms from Francois Jooste (phukraut(AT)hotmail.com), Mar 15 2002

A068949 Digit sums of A068809.

Original entry on oeis.org

1, 4, 9, 13, 16, 19, 22, 27, 31, 34, 36, 40, 43, 46, 49, 52, 54, 55, 58, 61, 63, 64, 67, 70, 73, 76, 79, 81, 82, 85, 88, 90, 91, 94, 97, 100, 103, 106, 108, 109, 112, 115, 117, 118, 121, 124, 127, 130, 133, 136, 139, 142, 144, 148, 153, 154, 157

Offset: 1

Francois Jooste (phukraut(AT)hotmail.com), Mar 15 2002

			a(4)=13 since A068809(4)=49, whose digit sum is 4+9 = 13.

Giovanni Resta, Table of n, a(n) for n = 1..80

Cf. A068809, A068950, A068952, A069324.

a(42)-a(57) from Kevin Buzzard (k.buzzard(AT)imperial.ac.uk), Jun 20 2008

A068947 Square roots of A068809.

Original entry on oeis.org

1, 2, 3, 7, 13, 17, 43, 63, 83, 167, 264, 313, 707, 836, 1667, 2236, 3114, 4472, 6833, 8167, 8937, 16667, 21886, 29614, 41833, 74833, 89437, 94863, 134164, 191833, 298327, 545793, 547613, 947617, 987917, 1643167, 3143167, 3162083, 5477133

Offset: 1

Francois Jooste (phukraut(AT)hotmail.com), Mar 15 2002

			13^2 = 169 = A068809(5), so a(5)=13.

Giovanni Resta, Table of n, a(n) for n = 1..80

Cf. A068809, A068948, A068949, A068950, A068952, A069324, A040047.

A007953 := proc(n) option remember: return add(d, d=convert(n, base, 10)): end: A068947 := proc(n) option remember: local k,p: if(n=1)then return 1: fi: k:=procname(n-1): p:=A007953(k^2): do k:=k+1: if(A007953(k^2)>p)then return k: fi: od: end: seq(A068947(n),n=1..20); # Nathaniel Johnston, May 04 2011

A069324 Primes in A068949.

Original entry on oeis.org

13, 19, 31, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 157, 163, 181, 193, 199, 211

Offset: 1

Francois Jooste (phukraut(AT)hotmail.com), Mar 15 2002

Differs from A040047 at the 13th term. - Kevin Buzzard (k.buzzard(AT)imperial.ac.uk), Jun 20 2008

			a(4)=43 since the fourth prime in A068949 is 43.

Cf. A068809, A068949, A068952, A040047.

disum(n)= { local(resul) ; resul=0 ; while(n>0, resul += n%10 ; n = (n-n%10)/10 ; ) ; return(resul) ; }
A069324(maxs)= { local(ssqu,su) ; su=1 ; for(s=1,maxs, ssqu=s^2 ; if (disum(ssqu) > su, su=disum(ssqu) ; if( isprime(su), print1(su,",") ; ) ; ) ; ) ; }
A069324(200000000) ; \\ R. J. Mathar, May 19 2006

a(12) from R. J. Mathar, May 19 2006
a(13)-a(14) from Kevin Buzzard (k.buzzard(AT)imperial.ac.uk), Jun 20 2008
a(15)-a(19) from Giovanni Resta, Jun 27 2018

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A068809 Squares with strictly increasing sum of digits.

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A068949 Digit sums of A068809.

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A068947 Square roots of A068809.

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A069324 Primes in A068949.

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